commit 1fe10f27fface9c05c9eb9a601df3c41ad174076
Author: Laureηt <laurent@fainsin.bzh>
Date:   Sat Jun 10 20:56:24 2023 +0200

    init

diff --git a/BE2019/.Naturelle.aux b/BE2019/.Naturelle.aux
new file mode 100755
index 0000000..5aa4821
--- /dev/null
+++ b/BE2019/.Naturelle.aux
@@ -0,0 +1,69 @@
+COQAUX1 b99e0673e480d281145bd0be828a8006 /home/lfainsin/1A/Modé/BE2019/Naturelle.v
+383 387 proof_build_time "0.000"
+0 0 E_imp_th "0.000"
+383 387 context_used ""
+383 387 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+916 920 proof_build_time "0.000"
+0 0 E_forall_th "0.000"
+916 920 context_used ""
+916 920 proof_check_time "0.000"
+1291 1295 proof_build_time "0.001"
+0 0 E_et_g_th "0.001"
+1291 1295 context_used ""
+1291 1295 proof_check_time "0.000"
+1601 1605 proof_build_time "0.001"
+0 0 E_et_d_th "0.001"
+1601 1605 context_used ""
+1601 1605 proof_check_time "0.000"
+1983 1987 proof_build_time "0.001"
+0 0 E_ou_th "0.001"
+1983 1987 context_used ""
+1983 1987 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+2806 2810 proof_build_time "0.001"
+0 0 E_exists_th "0.001"
+2806 2810 context_used ""
+2806 2810 proof_check_time "0.000"
+3280 3284 proof_build_time "0.000"
+0 0 E_antiT_th "0.000"
+3280 3284 context_used ""
+3280 3284 proof_check_time "0.000"
+3502 3506 proof_build_time "0.001"
+0 0 I_antiT_th "0.001"
+3502 3506 context_used ""
+3502 3506 proof_check_time "0.000"
+3683 3687 proof_build_time "0.000"
+0 0 I_non_th "0.000"
+3683 3687 context_used ""
+3683 3687 proof_check_time "0.000"
+4135 4158 context_used ""
+4135 4158 context_used ""
+4135 4158 context_used ""
+0 0 VernacProof "tac:no using:no"
+4398 4402 proof_build_time "0.003"
+0 0 Yoga "0.003"
+4398 4402 context_used ""
+4398 4402 proof_check_time "0.000"
+4404 4428 context_used ""
+4404 4428 context_used ""
+4557 4561 proof_build_time "0.001"
+0 0 contra "0.001"
+4557 4561 context_used ""
+4557 4561 proof_check_time "0.000"
+4642 4646 proof_build_time "0.001"
+0 0 P2nnP "0.001"
+4642 4646 context_used ""
+4642 4646 proof_check_time "0.000"
+4731 4735 proof_build_time "0.001"
+0 0 nnP2P "0.001"
+4731 4735 context_used ""
+4731 4735 proof_check_time "0.000"
+4737 4755 context_used ""
+4756 4786 context_used ""
+0 0 VernacProof "tac:no using:no"
+4984 4988 proof_build_time "0.002"
+0 0 Swap "0.002"
+4984 4988 context_used ""
+4984 4988 proof_check_time "0.000"
+0 0 vo_compile_time "0.617"
diff --git a/BE2019/Naturelle.glob b/BE2019/Naturelle.glob
new file mode 100755
index 0000000..db0c96e
--- /dev/null
+++ b/BE2019/Naturelle.glob
@@ -0,0 +1,254 @@
+DIGEST b99e0673e480d281145bd0be828a8006
+FNaturelle
+R15:23 Coq.Logic.Classical <> <> lib
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+prf 278:285 <> E_imp_th
+R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R337:339 Naturelle <> psi var
+R330:332 Naturelle <> phi var
+R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R322:324 Naturelle <> psi var
+R315:317 Naturelle <> phi var
+R443:450 Naturelle <> E_imp_th thm
+R521:528 Naturelle <> E_imp_th thm
+prf 816:826 <> E_forall_th
+R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R855:855 Naturelle <> A var
+R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R890:892 Naturelle <> phi var
+R894:894 Naturelle <> a var
+R880:882 Naturelle <> phi var
+R884:884 Naturelle <> x var
+R996:1006 Naturelle <> E_forall_th thm
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1105:1108 Coq.Init.Logic <> conj constr
+prf 1157:1165 <> E_et_g_th
+R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1210:1212 Naturelle <> phi var
+R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1195:1197 Naturelle <> phi var
+R1202:1204 Naturelle <> psi var
+R1352:1360 Naturelle <> E_et_g_th thm
+R1432:1440 Naturelle <> E_et_g_th thm
+prf 1465:1473 <> E_et_d_th
+R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1518:1520 Naturelle <> psi var
+R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1503:1505 Naturelle <> phi var
+R1510:1512 Naturelle <> psi var
+R1662:1670 Naturelle <> E_et_d_th thm
+R1743:1751 Naturelle <> E_et_d_th thm
+prf 1776:1782 <> E_ou_th
+R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1863:1865 Naturelle <> chi var
+R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1855:1857 Naturelle <> chi var
+R1848:1850 Naturelle <> psi var
+R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1839:1841 Naturelle <> chi var
+R1832:1834 Naturelle <> phi var
+R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R1816:1818 Naturelle <> phi var
+R1823:1825 Naturelle <> psi var
+R2042:2048 Naturelle <> E_ou_th thm
+R2124:2130 Naturelle <> E_ou_th thm
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2213:2221 Coq.Init.Logic <> or_introl constr
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2324:2332 Coq.Init.Logic <> or_intror constr
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2453:2460 Coq.Init.Logic <> ex_intro constr
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2597:2604 Coq.Init.Logic <> ex_intro constr
+prf 2669:2679 <> E_exists_th
+R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2708:2708 Naturelle <> A var
+R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2782:2784 Naturelle <> chi var
+R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2774:2776 Naturelle <> chi var
+R2765:2767 Naturelle <> phi var
+R2769:2769 Naturelle <> a var
+R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2744:2746 Naturelle <> phi var
+R2748:2748 Naturelle <> x var
+R2963:2973 Naturelle <> E_exists_th thm
+R3083:3085 Coq.Init.Logic <> not def
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
+prf 3209:3218 <> E_antiT_th
+R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3252:3254 Naturelle <> phi var
+R3243:3247 Coq.Init.Logic <> False ind
+R3340:3349 Naturelle <> E_antiT_th thm
+prf 3370:3379 <> I_antiT_th
+R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3421:3425 Coq.Init.Logic <> False ind
+R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3413:3415 Naturelle <> phi var
+R3404:3406 Naturelle <> phi var
+R3435:3437 Coq.Init.Logic <> not def
+R3551:3555 Coq.Init.Logic <> False ind
+R3551:3555 Coq.Init.Logic <> False ind
+R3567:3576 Naturelle <> I_antiT_th thm
+prf 3598:3605 <> I_non_th
+R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3649:3651 Naturelle <> phi var
+R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3638:3642 Coq.Init.Logic <> False ind
+R3631:3633 Naturelle <> phi var
+R3669:3671 Coq.Init.Logic <> not def
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3745:3752 Naturelle <> I_non_th thm
+R3801:3810 Naturelle <> I_antiT_th thm
+R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm
+var 4144:4144 <> E
+var 4146:4146 <> Y
+var 4148:4148 <> R
+prf 4168:4171 <> Yoga
+R4175:4175 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4203:4207 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4210:4213 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4214:4214 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4215:4215 Naturelle <> E defax
+R4208:4208 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4209:4209 Naturelle <> R defax
+R4176:4176 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R4190:4195 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R4202:4202 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R4178:4182 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4189:4189 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4184:4187 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R4183:4183 Naturelle <> Y defax
+R4188:4188 Naturelle <> R defax
+R4177:4177 Naturelle <> E defax
+R4197:4200 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4201:4201 Naturelle <> R defax
+R4196:4196 Naturelle <> Y defax
+R4263:4263 Naturelle <> R defax
+R4272:4272 Naturelle <> Y defax
+R4274:4274 Naturelle <> R defax
+R4285:4285 Naturelle <> E defax
+R4300:4303 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4304:4304 Naturelle <> R defax
+R4299:4299 Naturelle <> Y defax
+R4300:4303 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4304:4304 Naturelle <> R defax
+R4299:4299 Naturelle <> Y defax
+R4343:4346 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4348:4351 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R4347:4347 Naturelle <> Y defax
+R4352:4352 Naturelle <> R defax
+R4342:4342 Naturelle <> E defax
+R4343:4346 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4348:4351 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R4347:4347 Naturelle <> Y defax
+R4352:4352 Naturelle <> R defax
+R4342:4342 Naturelle <> E defax
+var 4413:4415 <> phi
+var 4417:4419 <> psi
+prf 4438:4443 <> contra
+R4447:4447 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4458:4463 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4476:4476 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4468:4471 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4472:4472 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4473:4475 Naturelle <> phi defax
+R4464:4464 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4465:4467 Naturelle <> psi defax
+R4451:4454 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4455:4457 Naturelle <> psi defax
+R4448:4450 Naturelle <> phi defax
+R4517:4519 Naturelle <> psi defax
+R4528:4530 Naturelle <> phi defax
+prf 4571:4575 <> P2nnP
+R4582:4585 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4586:4586 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4587:4587 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4588:4590 Naturelle <> phi defax
+R4579:4581 Naturelle <> phi defax
+R4621:4623 Naturelle <> phi defax
+prf 4656:4660 <> nnP2P
+R4670:4673 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4674:4676 Naturelle <> phi defax
+R4664:4664 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4665:4666 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4667:4669 Naturelle <> phi defax
+R4708:4708 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4709:4711 Naturelle <> phi defax
+R4708:4708 Coq.Init.Logic <> ::type_scope:'~'_x not
+R4709:4711 Naturelle <> phi defax
+var 4746:4746 <> A
+var 4765:4767 <> chi
+R4772:4775 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4777:4780 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4776:4776 Naturelle <> A defax
+R4771:4771 Naturelle <> A defax
+prf 4796:4799 <> Swap
+R4803:4803 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4831:4836 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4864:4864 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R4847:4853 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R4855:4856 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R4857:4859 Naturelle <> chi defax
+R4863:4863 Naturelle <> y var
+R4861:4861 Naturelle <> x var
+R4804:4810 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R4812:4813 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R4824:4826 Naturelle <> chi defax
+R4830:4830 Naturelle <> y var
+R4828:4828 Naturelle <> x var
+R4926:4926 Naturelle <> A defax
+R4929:4931 Naturelle <> chi defax
+R4935:4935 Naturelle <> y var
+R4933:4933 Naturelle <> x var
+R4926:4926 Naturelle <> A defax
+R4929:4931 Naturelle <> chi defax
+R4935:4935 Naturelle <> y var
+R4933:4933 Naturelle <> x var
diff --git a/BE2019/Naturelle.v b/BE2019/Naturelle.v
new file mode 100755
index 0000000..47b0dd7
--- /dev/null
+++ b/BE2019/Naturelle.v
@@ -0,0 +1,292 @@
+Require Export Classical.
+
+Ltac Hyp Nom := exact Nom.
+
+Ltac I_imp' :=
+  match goal with
+  | |- ?A -> ?B => let hyp := fresh "H" in intro hyp
+  | _           => fail
+  end.
+
+Ltac I_imp Nom :=
+  match goal with
+  | |- ?A -> ?B => intro Nom
+  | _           => fail
+  end.
+
+Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
+intros Pphi Ppsi Hphi2psi.
+Hyp Hphi2psi.
+Qed.
+
+Ltac E_imp' :=
+  match goal with
+  | |- ?P => eapply (E_imp_th _ P)
+  end.
+
+Ltac E_imp phi :=
+  match goal with
+  | |- ?P => apply (E_imp_th phi P)
+  end.
+
+Ltac I_forall' :=
+  match goal with
+  | |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
+  | _                      => fail
+  end.
+
+Ltac I_forall Nom :=
+  match goal with
+  | |- forall (x : ?A), ?P => intro Nom
+  | _                      => fail
+  end.
+
+Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
+Proof.
+firstorder.
+Qed.
+
+Ltac E_forall x :=
+  pattern x;
+  match goal with
+  | |- (?P x) => apply (E_forall_th _ P x)
+  | _         => fail
+  end.
+
+Ltac I_et :=
+  match goal with
+  | |- (?A /\ ?B) => apply (@conj A B)
+  | _             => fail
+  end.
+
+Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
+intros Pphi Ppsi Hphi_et_psi.
+elim Hphi_et_psi.
+intros Hphi Hpsi.
+Hyp Hphi.
+Qed.
+
+Ltac E_et_g' :=
+  match goal with
+  | |- ?P => eapply (E_et_g_th P _)
+  end.
+
+Ltac E_et_g psi :=
+  match goal with
+  | |- ?P => apply (E_et_g_th P psi)
+  end.
+
+Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
+intros Pphi Ppsi H_phi_et_psi.
+elim H_phi_et_psi.
+intros Hphi Hpsi.
+Hyp Hpsi.
+Qed.
+
+Ltac E_et_d' :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th _ P)
+  end.
+
+Ltac E_et_d phi :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th phi P)
+  end.
+
+Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
+intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
+elim Hphi_ou_psi.
+Hyp Hphi_imp_chi.
+Hyp Hpsi_imp_chi.
+Qed.
+
+Ltac E_ou' :=
+  match goal with
+  | |- ?P => eapply (E_ou_th _ _ P)
+  end.
+
+Ltac E_ou phi psi :=
+  match goal with
+  | |- ?P => apply (E_ou_th phi psi P)
+  end.
+
+Ltac I_ou_g :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_introl A B)
+  | _             => fail
+  end.
+
+Ltac I_ou_d :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_intror A B)
+  | _             => fail
+  end.
+
+Ltac I_exists' :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
+  | _                           => fail
+  end.
+
+Ltac I_exists t :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
+  | _                           => fail
+  end.
+
+Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
+Proof.
+firstorder.
+Qed.
+(*
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P)
+  end.
+*)
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
+  end.
+
+Ltac TE :=
+  unfold not;
+  match goal with
+  | |- (?P \/ (?P -> False)) => exact (classic P)
+  | _                        => fail
+  end.
+
+Theorem E_antiT_th : forall (phi : Prop), False -> phi.
+intros Pphi F.
+elim F.
+Qed.
+
+Ltac E_antiT :=
+  match goal with
+  | |- ?P => apply (E_antiT_th P)
+  end.
+
+Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
+unfold not.
+intro Pphi.
+intros Hphi Hnphi.
+cut Pphi.
+Hyp Hnphi.
+Hyp Hphi.
+Qed.
+
+Ltac I_antiT phi :=
+ match goal with
+ | |- False => apply (I_antiT_th phi)
+ end.
+
+Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
+intros.
+unfold not.
+exact H.
+Qed.
+
+Ltac I_non Nom :=
+ match goal with
+ | |- ~ ?P => apply (I_non_th P); intro Nom
+ end.
+
+Ltac E_non phi :=
+ apply (I_antiT_th phi).
+
+Ltac absurde Nom :=
+ match goal with
+ | |- ?P => apply (NNPP P); intro Nom
+ end.
+
+(*
+Ltac I_antiT phi := apply (I_antiT_th phi).
+
+Ltac absurde Nom phi :=
+match goal with
+| |- phi =>
+cut (phi \/ ~phi);
+[
+intros L;
+elim L;
+[
+auto
+|
+clear L;
+intro Nom;
+apply (E_antiT_th)
+]
+|
+apply (classic phi)
+]
+| _ => fail
+end.
+*)
+
+Variable E Y R  : Prop.
+
+Theorem Yoga : ((E -> (Y \/ R)) /\ (Y -> R)) -> ~R -> ~E.
+Proof.
+I_imp H1.
+I_imp H2.
+I_non H3.
+I_antiT R.
+ E_ou Y R.
+  E_imp E.
+   E_et_g (Y -> R).
+   Hyp H1.
+
+   Hyp H3.
+
+  E_et_d (E -> Y \/ R).
+  Hyp H1.
+
+  I_imp H4.
+  Hyp H4.
+ Hyp H2.
+Qed.
+
+Variable phi psi : Prop.
+
+Theorem contra : (phi -> psi) -> (~psi -> ~phi).
+I_imp H1.
+I_imp H2.
+I_non H3.
+I_antiT psi.
+E_imp phi.
+Hyp H1.
+Hyp H3.
+Hyp H2.
+Qed.
+
+Theorem P2nnP : phi -> ~~phi.
+I_imp H1.
+I_non H2.
+I_antiT phi.
+Hyp H1.
+Hyp H2.
+Qed.
+
+Theorem nnP2P : ~~ phi -> phi.
+I_imp H1.
+absurde H2.
+E_non (~phi).
+Hyp H2.
+Hyp H1.
+Qed.
+
+Variable A : Type.
+Variable chi : A -> A -> Prop.
+
+Theorem Swap : (exists y, forall x, chi x y) -> (forall x, exists y, chi x y).
+Proof.
+I_imp H1.
+I_forall x.
+E_exists (fun y => forall x : A, chi x y).
+ Hyp H1.
+
+ I_exists t.
+ E_forall x.
+ Hyp Ht.
+Qed.
+
diff --git a/BE2019/coq-exercice-1.v b/BE2019/coq-exercice-1.v
new file mode 100755
index 0000000..896ed57
--- /dev/null
+++ b/BE2019/coq-exercice-1.v
@@ -0,0 +1,23 @@
+Require Import Naturelle.
+Section Session1_2019_Logique_Exercice_1.
+
+Variable A B C : Prop.
+
+Theorem Exercice_1_Coq :  (A -> B -> C) -> ((A /\ B) -> C).
+intros.
+cut B.
+cut A.
+exact H.
+destruct H0.
+exact H0.
+destruct H0.
+exact H1.
+Qed.
+
+Theorem Exercice_1_Naturelle :  (A -> B -> C) -> ((A /\ B) -> C).
+Proof.
+(* A COMPLETER *)
+Qed.
+
+End Session1_2019_Logique_Exercice_1.
+
diff --git a/BE2019/coq-exercice-2.v b/BE2019/coq-exercice-2.v
new file mode 100755
index 0000000..78282cd
--- /dev/null
+++ b/BE2019/coq-exercice-2.v
@@ -0,0 +1,19 @@
+Require Import Naturelle.
+Section Session1_2019_Logique_Exercice_2.
+
+Variable A B : Prop.
+
+Theorem Exercice_2_Coq : (~A) \/ B -> (~A) \/ (A /\ B).
+intros.
+right.
+split.
+
+Qed.
+
+Theorem Exercice_2_Naturelle : (~A) \/ B -> (~A) \/ (A /\ B).
+Proof.
+(* A COMPLETER *)
+Qed.
+
+End Session1_2019_Logique_Exercice_2.
+
diff --git a/BE2019/coq-exercice-3.v b/BE2019/coq-exercice-3.v
new file mode 100755
index 0000000..c4c74e0
--- /dev/null
+++ b/BE2019/coq-exercice-3.v
@@ -0,0 +1,102 @@
+Section Session1_2019_Induction_Exercice_3.
+
+(* Déclaration d’un domaine pour les éléments des listes *)
+Variable A : Set.
+
+(* Déclaration d'un type liste générique d'éléments de type E *)
+Inductive liste (E : Set) : Set :=
+Nil
+: liste E
+| Cons : E -> liste E -> liste E.
+
+(* Déclaration du nom de la fonction append *)
+Variable append_spec : forall E : Set, liste E -> liste E -> liste E.
+
+(* Spécification du comportement de append pour Nil en premier paramètre *)
+Axiom append_Nil : forall E : Set, forall (l : liste E), append_spec E (Nil E) l = l.
+
+(* Spécification du comportement de append pour Cons en premier paramètre *)
+Axiom append_Cons : forall E : Set, forall (t : E), forall (q l : liste E),
+   append_spec E ((Cons E) t q) l = (Cons E) t (append_spec E q l).
+
+(* Spécification du comportement de append pour Nil en second paramètre *)
+Axiom append_Nil_right : forall E : Set, forall (l : liste E), (append_spec E l (Nil E)) = l.
+
+(* append est associative à gauche et à droite *)
+Axiom append_associative : forall E : Set, forall (l1 l2 l3 : liste E),
+   (append_spec E l1 (append_spec E l2 l3)) = (append_spec E (append_spec E l1 l2) l3).
+
+(* Déclaration du nom de la fonction flatten *)
+Variable flatten_spec : forall E : Set, liste (liste E) -> liste E.
+
+(* Spécification du comportement de flatten pour Nil *)
+Axiom flatten_Nil : forall E : Set, flatten_spec E (Nil (liste E)) = (Nil E).
+
+(* Spécification du comportement de flatten pour Cons *)
+Axiom flatten_Cons : forall E : Set, forall (t : liste E), forall (q : liste (liste E)),
+  flatten_spec E (Cons (liste E) t q) = append_spec E t (flatten_spec E q).
+
+(* Déclaration du nom de la fonction split *)
+Variable split_spec : forall E : Set, liste E -> liste (liste E).
+
+(* Spécification du comportement de split pour Nil *)
+Axiom split_Nil : forall E : Set, split_spec E (Nil E) = (Nil (liste E)).
+
+(* Spécification du comportement de split pour Cons *)
+Axiom split_Cons : forall E : Set, forall (t : E), forall (q : liste E),
+  split_spec E (Cons E t q) = Cons (liste E) (Cons E t (Nil E)) (split_spec E q).
+
+(* Cohérence de flatten et de split : flatten(split(l)) = l*)
+Theorem flatten_split_consistency : forall E : Set, forall (l : liste E),
+   flatten_spec E (split_spec E l) = l.
+intros.
+induction l.
+rewrite split_Nil.
+rewrite flatten_Nil.
+reflexivity.
+rewrite split_Cons.
+rewrite flatten_Cons.
+rewrite IHl.
+rewrite append_Cons.
+rewrite append_Nil.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction append *)
+Fixpoint append_impl (E : Set) (l1 l2 : liste E) {struct l1} : liste E :=
+match l1 with
+Nil _ => l2
+| (Cons _ t1 q1) => (Cons E t1 (append_impl E q1 l2))
+end.
+
+Theorem append_correctness : forall E : Set, forall (l1 l2 : liste E),
+(append_spec E l1 l2) = (append_impl E l1 l2).
+intro TE.
+induction l1.
+intro Hl2.
+rewrite append_Nil.
+simpl.
+reflexivity.
+intro Hl2.
+rewrite append_Cons.
+simpl.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction flatten *)
+Fixpoint flatten_impl (E : Set) (l : liste (liste E)) {struct l} : liste E :=
+  match l with
+    Nil => Nil
+    | (Cons t1 q1) => (Cons t1 (flatten_impl q1 l2))
+end.
+
+
+(* Correction de l'implantation de flatten par rapport à sa spécification *)
+Theorem flatten_correctness : forall E : Set, forall (l : liste (liste E)),
+   (flatten_spec E l) = (flatten_impl E l).
+Proof.
+(* A COMPLETER *)
+Qed.
+
+End Session1_2019_Induction_Exercice_3.
diff --git a/BE2019/why3-exercice-4.mlw b/BE2019/why3-exercice-4.mlw
new file mode 100755
index 0000000..335f087
--- /dev/null
+++ b/BE2019/why3-exercice-4.mlw
@@ -0,0 +1,24 @@
+(* BE : Session 1 2019 *)
+(* Implémentation de la fonction somme des premiers entiers par un algorithme ascendant *)
+
+module Somme
+
+  use int.Int
+  use int.ComputerDivision
+  use ref.Refint
+
+  let somme (n: int) : int
+    requires { n >= 0 }
+    ensures  { 2*result = n*(n+1) }
+  =
+    let i = ref 0 in
+    let r = ref 0 in
+    while  (!i < n) do
+      invariant { 2*!r = !i*(!i+1) }
+      variant   { n - !i }
+      i := (!i) + 1;
+      r := (!r) + (!i)
+    done;
+    !r
+
+end
diff --git a/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_1.v b/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_1.v
new file mode 100755
index 0000000..f9ef867
--- /dev/null
+++ b/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_1.v
@@ -0,0 +1,44 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+Require int.Abs.
+Require int.ComputerDivision.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter n: Z.
+
+Parameter r: Z.
+
+Parameter i: Z.
+
+Axiom H : (i < n)%Z.
+
+Parameter i1: Z.
+
+Axiom H1 : (i1 = (i + 1%Z)%Z).
+
+Parameter r1: Z.
+
+Axiom H2 : (r1 = (r + i1)%Z).
+
+(* Why3 goal *)
+Theorem VC_somme : False.
+Proof.
+
+
+Qed.
+
diff --git a/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_2.v b/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_2.v
new file mode 100755
index 0000000..f9ef867
--- /dev/null
+++ b/BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_2.v
@@ -0,0 +1,44 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+Require int.Abs.
+Require int.ComputerDivision.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter n: Z.
+
+Parameter r: Z.
+
+Parameter i: Z.
+
+Axiom H : (i < n)%Z.
+
+Parameter i1: Z.
+
+Axiom H1 : (i1 = (i + 1%Z)%Z).
+
+Parameter r1: Z.
+
+Axiom H2 : (r1 = (r + i1)%Z).
+
+(* Why3 goal *)
+Theorem VC_somme : False.
+Proof.
+
+
+Qed.
+
diff --git a/BE2019/why3-exercice-4/why3session.xml b/BE2019/why3-exercice-4/why3session.xml
new file mode 100755
index 0000000..b5b65e5
--- /dev/null
+++ b/BE2019/why3-exercice-4/why3session.xml
@@ -0,0 +1,39 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.9.1" timelimit="0" steplimit="0" memlimit="0"/>
+<prover id="5" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<file>
+<path name=".."/>
+<path name="why3-exercice-4.mlw"/>
+<theory name="Somme">
+ <goal name="VC somme" expl="VC for somme">
+ <proof prover="1"><result status="unknown" time="0.05"/></proof>
+ <transf name="split_vc" >
+  <goal name="VC somme.0" expl="loop invariant init" proved="true">
+  <proof prover="1"><result status="valid" time="0.00" steps="1"/></proof>
+  </goal>
+  <goal name="VC somme.1" expl="loop variant decrease">
+  <proof prover="0"><result status="unknown" time="0.07"/></proof>
+  <proof prover="1"><result status="unknown" time="0.04"/></proof>
+  <proof prover="2"><result status="timeout" time="5.00"/></proof>
+  <proof prover="3"><result status="unknown" time="0.01"/></proof>
+  <proof prover="4" obsolete="true" edited="why3mnexercicemn4_Somme_VC_somme_2.v"><result status="unknown" time="0.00" steps="0"/></proof>
+  <proof prover="5"><result status="timeout" time="5.00"/></proof>
+  </goal>
+  <goal name="VC somme.2" expl="loop invariant preservation" proved="true">
+  <proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
+  </goal>
+  <goal name="VC somme.3" expl="postcondition" proved="true">
+  <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/BE2020/.Naturelle.aux b/BE2020/.Naturelle.aux
new file mode 100755
index 0000000..c422526
--- /dev/null
+++ b/BE2020/.Naturelle.aux
@@ -0,0 +1,40 @@
+COQAUX1 3e03a7b5b5c26232f0f3e8f10219c975 /home/lfainsin/1A/Modé/BE2020/Naturelle.v
+383 387 proof_build_time "0.000"
+0 0 E_imp_th "0.000"
+383 387 context_used ""
+383 387 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+916 920 proof_build_time "0.000"
+0 0 E_forall_th "0.000"
+916 920 context_used ""
+916 920 proof_check_time "0.000"
+1291 1295 proof_build_time "0.001"
+0 0 E_et_g_th "0.001"
+1291 1295 context_used ""
+1291 1295 proof_check_time "0.000"
+1601 1605 proof_build_time "0.000"
+0 0 E_et_d_th "0.000"
+1601 1605 context_used ""
+1601 1605 proof_check_time "0.000"
+1983 1987 proof_build_time "0.001"
+0 0 E_ou_th "0.001"
+1983 1987 context_used ""
+1983 1987 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+2806 2810 proof_build_time "0.001"
+0 0 E_exists_th "0.001"
+2806 2810 context_used ""
+2806 2810 proof_check_time "0.000"
+3280 3284 proof_build_time "0.000"
+0 0 E_antiT_th "0.000"
+3280 3284 context_used ""
+3280 3284 proof_check_time "0.000"
+3502 3506 proof_build_time "0.001"
+0 0 I_antiT_th "0.001"
+3502 3506 context_used ""
+3502 3506 proof_check_time "0.000"
+3683 3687 proof_build_time "0.000"
+0 0 I_non_th "0.000"
+3683 3687 context_used ""
+3683 3687 proof_check_time "0.000"
+0 0 vo_compile_time "0.107"
diff --git a/BE2020/Naturelle.glob b/BE2020/Naturelle.glob
new file mode 100755
index 0000000..3c23cb5
--- /dev/null
+++ b/BE2020/Naturelle.glob
@@ -0,0 +1,150 @@
+DIGEST 3e03a7b5b5c26232f0f3e8f10219c975
+FNaturelle
+R15:23 Coq.Logic.Classical <> <> lib
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+prf 278:285 <> E_imp_th
+R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R337:339 Naturelle <> psi var
+R330:332 Naturelle <> phi var
+R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R322:324 Naturelle <> psi var
+R315:317 Naturelle <> phi var
+R443:450 Naturelle <> E_imp_th thm
+R521:528 Naturelle <> E_imp_th thm
+prf 816:826 <> E_forall_th
+R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R855:855 Naturelle <> A var
+R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R890:892 Naturelle <> phi var
+R894:894 Naturelle <> a var
+R880:882 Naturelle <> phi var
+R884:884 Naturelle <> x var
+R996:1006 Naturelle <> E_forall_th thm
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1105:1108 Coq.Init.Logic <> conj constr
+prf 1157:1165 <> E_et_g_th
+R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1210:1212 Naturelle <> phi var
+R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1195:1197 Naturelle <> phi var
+R1202:1204 Naturelle <> psi var
+R1352:1360 Naturelle <> E_et_g_th thm
+R1432:1440 Naturelle <> E_et_g_th thm
+prf 1465:1473 <> E_et_d_th
+R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1518:1520 Naturelle <> psi var
+R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1503:1505 Naturelle <> phi var
+R1510:1512 Naturelle <> psi var
+R1662:1670 Naturelle <> E_et_d_th thm
+R1743:1751 Naturelle <> E_et_d_th thm
+prf 1776:1782 <> E_ou_th
+R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1863:1865 Naturelle <> chi var
+R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1855:1857 Naturelle <> chi var
+R1848:1850 Naturelle <> psi var
+R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1839:1841 Naturelle <> chi var
+R1832:1834 Naturelle <> phi var
+R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R1816:1818 Naturelle <> phi var
+R1823:1825 Naturelle <> psi var
+R2042:2048 Naturelle <> E_ou_th thm
+R2124:2130 Naturelle <> E_ou_th thm
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2213:2221 Coq.Init.Logic <> or_introl constr
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2324:2332 Coq.Init.Logic <> or_intror constr
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2453:2460 Coq.Init.Logic <> ex_intro constr
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2597:2604 Coq.Init.Logic <> ex_intro constr
+prf 2669:2679 <> E_exists_th
+R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2708:2708 Naturelle <> A var
+R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2782:2784 Naturelle <> chi var
+R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2774:2776 Naturelle <> chi var
+R2765:2767 Naturelle <> phi var
+R2769:2769 Naturelle <> a var
+R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2744:2746 Naturelle <> phi var
+R2748:2748 Naturelle <> x var
+R2963:2973 Naturelle <> E_exists_th thm
+R3083:3085 Coq.Init.Logic <> not def
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
+prf 3209:3218 <> E_antiT_th
+R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3252:3254 Naturelle <> phi var
+R3243:3247 Coq.Init.Logic <> False ind
+R3340:3349 Naturelle <> E_antiT_th thm
+prf 3370:3379 <> I_antiT_th
+R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3421:3425 Coq.Init.Logic <> False ind
+R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3413:3415 Naturelle <> phi var
+R3404:3406 Naturelle <> phi var
+R3435:3437 Coq.Init.Logic <> not def
+R3551:3555 Coq.Init.Logic <> False ind
+R3551:3555 Coq.Init.Logic <> False ind
+R3567:3576 Naturelle <> I_antiT_th thm
+prf 3598:3605 <> I_non_th
+R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3649:3651 Naturelle <> phi var
+R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3638:3642 Coq.Init.Logic <> False ind
+R3631:3633 Naturelle <> phi var
+R3669:3671 Coq.Init.Logic <> not def
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3745:3752 Naturelle <> I_non_th thm
+R3801:3810 Naturelle <> I_antiT_th thm
+R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm
diff --git a/BE2020/Naturelle.v b/BE2020/Naturelle.v
new file mode 100755
index 0000000..b1d6533
--- /dev/null
+++ b/BE2020/Naturelle.v
@@ -0,0 +1,224 @@
+Require Export Classical.
+
+Ltac Hyp Nom := exact Nom.
+
+Ltac I_imp' :=
+  match goal with
+  | |- ?A -> ?B => let hyp := fresh "H" in intro hyp
+  | _           => fail
+  end.
+
+Ltac I_imp Nom :=
+  match goal with
+  | |- ?A -> ?B => intro Nom
+  | _           => fail
+  end.
+
+Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
+intros Pphi Ppsi Hphi2psi.
+Hyp Hphi2psi.
+Qed.
+
+Ltac E_imp' :=
+  match goal with
+  | |- ?P => eapply (E_imp_th _ P)
+  end.
+
+Ltac E_imp phi :=
+  match goal with
+  | |- ?P => apply (E_imp_th phi P)
+  end.
+
+Ltac I_forall' :=
+  match goal with
+  | |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
+  | _                      => fail
+  end.
+
+Ltac I_forall Nom :=
+  match goal with
+  | |- forall (x : ?A), ?P => intro Nom
+  | _                      => fail
+  end.
+
+Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
+Proof.
+firstorder.
+Qed.
+
+Ltac E_forall x :=
+  pattern x;
+  match goal with
+  | |- (?P x) => apply (E_forall_th _ P x)
+  | _         => fail
+  end.
+
+Ltac I_et :=
+  match goal with
+  | |- (?A /\ ?B) => apply (@conj A B)
+  | _             => fail
+  end.
+
+Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
+intros Pphi Ppsi Hphi_et_psi.
+elim Hphi_et_psi.
+intros Hphi Hpsi.
+Hyp Hphi.
+Qed.
+
+Ltac E_et_g' :=
+  match goal with
+  | |- ?P => eapply (E_et_g_th P _)
+  end.
+
+Ltac E_et_g psi :=
+  match goal with
+  | |- ?P => apply (E_et_g_th P psi)
+  end.
+
+Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
+intros Pphi Ppsi H_phi_et_psi.
+elim H_phi_et_psi.
+intros Hphi Hpsi.
+Hyp Hpsi.
+Qed.
+
+Ltac E_et_d' :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th _ P)
+  end.
+
+Ltac E_et_d phi :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th phi P)
+  end.
+
+Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
+intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
+elim Hphi_ou_psi.
+Hyp Hphi_imp_chi.
+Hyp Hpsi_imp_chi.
+Qed.
+
+Ltac E_ou' :=
+  match goal with
+  | |- ?P => eapply (E_ou_th _ _ P)
+  end.
+
+Ltac E_ou phi psi :=
+  match goal with
+  | |- ?P => apply (E_ou_th phi psi P)
+  end.
+
+Ltac I_ou_g :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_introl A B)
+  | _             => fail
+  end.
+
+Ltac I_ou_d :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_intror A B)
+  | _             => fail
+  end.
+
+Ltac I_exists' :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
+  | _                           => fail
+  end.
+
+Ltac I_exists t :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
+  | _                           => fail
+  end.
+
+Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
+Proof.
+firstorder.
+Qed.
+(*
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P)
+  end.
+*)
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
+  end.
+
+Ltac TE :=
+  unfold not;
+  match goal with
+  | |- (?P \/ (?P -> False)) => exact (classic P)
+  | _                        => fail
+  end.
+
+Theorem E_antiT_th : forall (phi : Prop), False -> phi.
+intros Pphi F.
+elim F.
+Qed.
+
+Ltac E_antiT :=
+  match goal with
+  | |- ?P => apply (E_antiT_th P)
+  end.
+
+Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
+unfold not.
+intro Pphi.
+intros Hphi Hnphi.
+cut Pphi.
+Hyp Hnphi.
+Hyp Hphi.
+Qed.
+
+Ltac I_antiT phi :=
+ match goal with
+ | |- False => apply (I_antiT_th phi)
+ end.
+
+Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
+intros.
+unfold not.
+exact H.
+Qed.
+
+Ltac I_non Nom :=
+ match goal with
+ | |- ~ ?P => apply (I_non_th P); intro Nom
+ end.
+
+Ltac E_non phi :=
+ apply (I_antiT_th phi).
+
+Ltac absurde Nom :=
+ match goal with
+ | |- ?P => apply (NNPP P); intro Nom
+ end.
+
+(*
+Ltac I_antiT phi := apply (I_antiT_th phi).
+
+Ltac absurde Nom phi :=
+match goal with
+| |- phi =>
+cut (phi \/ ~phi);
+[
+intros L;
+elim L;
+[
+auto
+|
+clear L;
+intro Nom;
+apply (E_antiT_th)
+]
+|
+apply (classic phi)
+]
+| _ => fail
+end.
+*)
diff --git a/BE2020/coq_exercice_1.v b/BE2020/coq_exercice_1.v
new file mode 100755
index 0000000..5b67f60
--- /dev/null
+++ b/BE2020/coq_exercice_1.v
@@ -0,0 +1,41 @@
+Require Import Naturelle.
+Section Session1_2020_Logique_Exercice_1.
+
+Variable A B C : Prop.
+
+Theorem Exercice_1_Naturelle :  ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
+I_imp H1.
+I_imp H2.
+E_imp A.
+E_ou (A -> C) (B -> C).
+Hyp H1.
+trivial.
+I_imp H3.
+I_imp H4.
+E_imp B.
+Hyp H3.
+E_et_d A.
+Hyp H2.
+E_et_g B.
+Hyp H2.
+Qed.
+
+Theorem Exercice_1_Coq : ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
+intros.
+destruct H.
+destruct H0.
+cut A.
+exact H.
+exact H0.
+cut B.
+exact H.
+cut (A /\ B).
+intro H2.
+elim H2.
+intros HA HB.
+exact HB.
+exact H0.
+Qed.
+
+End Session1_2020_Logique_Exercice_1.
+
diff --git a/BE2020/coq_exercice_2.v b/BE2020/coq_exercice_2.v
new file mode 100755
index 0000000..46e448e
--- /dev/null
+++ b/BE2020/coq_exercice_2.v
@@ -0,0 +1,17 @@
+Require Import Naturelle.
+Section Session1_2020_Logique_Exercice_2.
+
+Variable A B : Prop.
+
+Theorem Exercice_2_Naturelle : (A -> B) -> ((~A) \/ B).
+Proof.
+(* A COMPLETER *)
+Qed.
+
+Theorem Exercice_2_Coq : (A -> B) -> ((~A) \/ B).
+Proof.
+(* A COMPLETER *)
+Qed.
+
+End Session1_2020_Logique_Exercice_2.
+
diff --git a/BE2020/coq_exercice_3.v b/BE2020/coq_exercice_3.v
new file mode 100755
index 0000000..6237cb2
--- /dev/null
+++ b/BE2020/coq_exercice_3.v
@@ -0,0 +1,91 @@
+Section Session1_2020_Induction_Exercice_3.
+
+(* Déclaration d’un domaine pour les éléments des listes *)
+Variable A : Set.
+
+Inductive entier : Set :=
+Zero : entier
+| Succ : entier -> entier.
+
+(* Déclaration du nom de la fonction somme *)
+Variable somme_spec : entier -> entier -> entier.
+
+(* Spécification du comportement de somme pour Zero en premier paramètre *)
+Axiom somme_Zero : forall (n : entier), somme_spec Zero n = n.
+
+(* Spécification du comportement de somme pour Succ en premier paramètre *)
+Axiom somme_Succ : forall (n m : entier),
+  somme_spec (Succ n) m = Succ (somme_spec n m).
+
+(* somme est associative à gauche et à droite *)
+Axiom somme_associative : forall (n1 n2 n3 : entier),
+   (somme_spec n1 (somme_spec n2 n3)) = (somme_spec (somme_spec n1 n2) n3).
+
+Inductive liste : Set :=
+Nil
+: liste
+| Cons : A -> liste -> liste.
+
+(* Déclaration du nom de la fonction append *)
+Variable append_spec : liste -> liste -> liste.
+
+(* Spécification du comportement de append pour Nil en premier paramètre *)
+Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
+
+(* Spécification du comportement de append pour Cons en premier paramètre *)
+Axiom append_Cons : forall (t : A), forall (q l : liste),
+   append_spec (Cons t q) l = Cons t (append_spec q l).
+
+(* append est associative à gauche et à droite *)
+Axiom append_associative : forall (l1 l2 l3 : liste),
+   (append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
+
+(* Déclaration du nom de la fonction taille *)
+Variable taille_spec : liste -> entier.
+
+(* Spécification du comportement de taille pour Nil en paramètre *)
+Axiom taille_Nil : taille_spec Nil = Zero .
+
+(* Spécification du comportement de taille pour Cons en paramètre *)
+Axiom taille_Cons : forall (t : A), forall (q : liste),
+    taille_spec (Cons t q) = Succ (taille_spec q) .
+
+
+(* taille commute avec append *)
+Theorem taille_append : forall (l1 l2 : liste), 
+(taille_spec (append_spec l1 l2)) = (somme_spec (taille_spec l1) (taille_spec l2)).
+intros.
+induction l1.
+rewrite append_Nil.
+rewrite taille_Nil.
+rewrite somme_Zero.
+reflexivity.
+rewrite append_Cons.
+rewrite taille_Cons.
+rewrite taille_Cons.
+rewrite somme_Succ.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction taille *)
+Fixpoint taille_impl (l : liste) {struct l} : entier :=
+   match l with
+      Nil => Zero
+      | (Cons t q) => (Succ (taille_impl q))
+end.
+
+Theorem taille_correctness : forall (l : liste),
+   (taille_spec l) = (taille_impl l).
+intros.
+induction l.
+simpl taille_impl.
+rewrite taille_Nil.
+reflexivity.
+simpl taille_impl.
+rewrite taille_Cons.
+rewrite IHl.
+reflexivity.
+Qed.
+
+End Session1_2020_Induction_Exercice_3.
diff --git a/BE2020/why3_exercice_4.mlw b/BE2020/why3_exercice_4.mlw
new file mode 100755
index 0000000..3ab8361
--- /dev/null
+++ b/BE2020/why3_exercice_4.mlw
@@ -0,0 +1,23 @@
+(* BE : Session 1 2020 *)
+(* Implémentation de la fonction carre d'un entier naturel par un algorithme inspiré des identités remarquables *)
+
+module Carre
+
+  use int.Int
+  use ref.Refint
+
+  let carre (n: int) : int
+    requires { 0 <= n }
+    ensures  { !r = n*n }
+  =
+    let x = ref n in
+    let r = ref 0 in
+    while (!x <> 0) do
+      invariant { !r + (!x)*(!x) = n*n && 0 <= !x }
+      variant   { !x }
+      r := (!r) + 2 * (!x) - 1;
+      x := (!x) - 1
+    done;
+    !r
+
+end
\ No newline at end of file
diff --git a/BE2020/why3_exercice_4/why3session.xml b/BE2020/why3_exercice_4/why3session.xml
new file mode 100755
index 0000000..22a58ee
--- /dev/null
+++ b/BE2020/why3_exercice_4/why3session.xml
@@ -0,0 +1,36 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<file>
+<path name=".."/>
+<path name="why3_exercice_4.mlw"/>
+<theory name="Carre">
+ <goal name="VC carre" expl="VC for carre">
+ <transf name="split_vc" >
+  <goal name="VC carre.0" expl="loop invariant init" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="1"/></proof>
+  </goal>
+  <goal name="VC carre.1" expl="loop variant decrease">
+  <proof prover="0"><result status="unknown" time="0.01"/></proof>
+  <proof prover="1"><result status="unknown" time="0.12"/></proof>
+  <proof prover="2"><result status="timeout" time="5.00"/></proof>
+  <proof prover="3"><result status="unknown" time="0.02"/></proof>
+  <proof prover="4"><result status="timeout" time="5.00"/></proof>
+  </goal>
+  <goal name="VC carre.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="4"/></proof>
+  </goal>
+  <goal name="VC carre.3" expl="postcondition" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP1/.Naturelle.aux b/TP1/.Naturelle.aux
new file mode 100755
index 0000000..a8bbca0
--- /dev/null
+++ b/TP1/.Naturelle.aux
@@ -0,0 +1,40 @@
+COQAUX1 f13e540aa0997388dd1408b0662438d6 /home/lfainsin/1A/Modé/TP1/Naturelle.v
+383 387 proof_build_time "0.001"
+0 0 E_imp_th "0.001"
+383 387 context_used ""
+383 387 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+916 920 proof_build_time "0.001"
+0 0 E_forall_th "0.001"
+916 920 context_used ""
+916 920 proof_check_time "0.000"
+1291 1295 proof_build_time "0.001"
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+1291 1295 context_used ""
+1291 1295 proof_check_time "0.000"
+1601 1605 proof_build_time "0.001"
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+1601 1605 context_used ""
+1601 1605 proof_check_time "0.000"
+1983 1987 proof_build_time "0.001"
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+1983 1987 context_used ""
+1983 1987 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+2806 2810 proof_build_time "0.001"
+0 0 E_exists_th "0.001"
+2806 2810 context_used ""
+2806 2810 proof_check_time "0.000"
+3280 3284 proof_build_time "0.000"
+0 0 E_antiT_th "0.000"
+3280 3284 context_used ""
+3280 3284 proof_check_time "0.000"
+3502 3506 proof_build_time "0.001"
+0 0 I_antiT_th "0.001"
+3502 3506 context_used ""
+3502 3506 proof_check_time "0.000"
+3683 3687 proof_build_time "0.000"
+0 0 I_non_th "0.000"
+3683 3687 context_used ""
+3683 3687 proof_check_time "0.000"
+0 0 vo_compile_time "0.713"
diff --git a/TP1/Naturelle.glob b/TP1/Naturelle.glob
new file mode 100755
index 0000000..df9312d
--- /dev/null
+++ b/TP1/Naturelle.glob
@@ -0,0 +1,150 @@
+DIGEST f13e540aa0997388dd1408b0662438d6
+FNaturelle
+R15:23 Coq.Logic.Classical <> <> lib
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+prf 278:285 <> E_imp_th
+R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R337:339 Naturelle <> psi var
+R330:332 Naturelle <> phi var
+R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R322:324 Naturelle <> psi var
+R315:317 Naturelle <> phi var
+R443:450 Naturelle <> E_imp_th thm
+R521:528 Naturelle <> E_imp_th thm
+prf 816:826 <> E_forall_th
+R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R855:855 Naturelle <> A var
+R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R890:892 Naturelle <> phi var
+R894:894 Naturelle <> a var
+R880:882 Naturelle <> phi var
+R884:884 Naturelle <> x var
+R996:1006 Naturelle <> E_forall_th thm
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1105:1108 Coq.Init.Logic <> conj constr
+prf 1157:1165 <> E_et_g_th
+R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1210:1212 Naturelle <> phi var
+R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1195:1197 Naturelle <> phi var
+R1202:1204 Naturelle <> psi var
+R1352:1360 Naturelle <> E_et_g_th thm
+R1432:1440 Naturelle <> E_et_g_th thm
+prf 1465:1473 <> E_et_d_th
+R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1518:1520 Naturelle <> psi var
+R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1503:1505 Naturelle <> phi var
+R1510:1512 Naturelle <> psi var
+R1662:1670 Naturelle <> E_et_d_th thm
+R1743:1751 Naturelle <> E_et_d_th thm
+prf 1776:1782 <> E_ou_th
+R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1863:1865 Naturelle <> chi var
+R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1855:1857 Naturelle <> chi var
+R1848:1850 Naturelle <> psi var
+R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1839:1841 Naturelle <> chi var
+R1832:1834 Naturelle <> phi var
+R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R1816:1818 Naturelle <> phi var
+R1823:1825 Naturelle <> psi var
+R2042:2048 Naturelle <> E_ou_th thm
+R2124:2130 Naturelle <> E_ou_th thm
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2213:2221 Coq.Init.Logic <> or_introl constr
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2324:2332 Coq.Init.Logic <> or_intror constr
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2453:2460 Coq.Init.Logic <> ex_intro constr
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2597:2604 Coq.Init.Logic <> ex_intro constr
+prf 2669:2679 <> E_exists_th
+R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2708:2708 Naturelle <> A var
+R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2782:2784 Naturelle <> chi var
+R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2774:2776 Naturelle <> chi var
+R2765:2767 Naturelle <> phi var
+R2769:2769 Naturelle <> a var
+R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2744:2746 Naturelle <> phi var
+R2748:2748 Naturelle <> x var
+R2963:2973 Naturelle <> E_exists_th thm
+R3083:3085 Coq.Init.Logic <> not def
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
+prf 3209:3218 <> E_antiT_th
+R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3252:3254 Naturelle <> phi var
+R3243:3247 Coq.Init.Logic <> False ind
+R3340:3349 Naturelle <> E_antiT_th thm
+prf 3370:3379 <> I_antiT_th
+R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3421:3425 Coq.Init.Logic <> False ind
+R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3413:3415 Naturelle <> phi var
+R3404:3406 Naturelle <> phi var
+R3435:3437 Coq.Init.Logic <> not def
+R3551:3555 Coq.Init.Logic <> False ind
+R3551:3555 Coq.Init.Logic <> False ind
+R3567:3576 Naturelle <> I_antiT_th thm
+prf 3598:3605 <> I_non_th
+R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3649:3651 Naturelle <> phi var
+R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3638:3642 Coq.Init.Logic <> False ind
+R3631:3633 Naturelle <> phi var
+R3669:3671 Coq.Init.Logic <> not def
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3745:3752 Naturelle <> I_non_th thm
+R3801:3810 Naturelle <> I_antiT_th thm
+R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm
diff --git a/TP1/Naturelle.v b/TP1/Naturelle.v
new file mode 100755
index 0000000..0546e4d
--- /dev/null
+++ b/TP1/Naturelle.v
@@ -0,0 +1,225 @@
+Require Export Classical.
+
+Ltac Hyp Nom := exact Nom.
+
+Ltac I_imp' :=
+  match goal with
+  | |- ?A -> ?B => let hyp := fresh "H" in intro hyp
+  | _           => fail
+  end.
+
+Ltac I_imp Nom :=
+  match goal with
+  | |- ?A -> ?B => intro Nom
+  | _           => fail
+  end.
+
+Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
+intros Pphi Ppsi Hphi2psi.
+Hyp Hphi2psi.
+Qed.
+
+Ltac E_imp' :=
+  match goal with
+  | |- ?P => eapply (E_imp_th _ P)
+  end.
+
+Ltac E_imp phi :=
+  match goal with
+  | |- ?P => apply (E_imp_th phi P)
+  end.
+
+Ltac I_forall' :=
+  match goal with
+  | |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
+  | _                      => fail
+  end.
+
+Ltac I_forall Nom :=
+  match goal with
+  | |- forall (x : ?A), ?P => intro Nom
+  | _                      => fail
+  end.
+
+Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
+Proof.
+firstorder.
+Qed.
+
+Ltac E_forall x :=
+  pattern x;
+  match goal with
+  | |- (?P x) => apply (E_forall_th _ P x)
+  | _         => fail
+  end.
+
+Ltac I_et :=
+  match goal with
+  | |- (?A /\ ?B) => apply (@conj A B)
+  | _             => fail
+  end.
+
+Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
+intros Pphi Ppsi Hphi_et_psi.
+elim Hphi_et_psi.
+intros Hphi Hpsi.
+Hyp Hphi.
+Qed.
+
+Ltac E_et_g' :=
+  match goal with
+  | |- ?P => eapply (E_et_g_th P _)
+  end.
+
+Ltac E_et_g psi :=
+  match goal with
+  | |- ?P => apply (E_et_g_th P psi)
+  end.
+
+Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
+intros Pphi Ppsi H_phi_et_psi.
+elim H_phi_et_psi.
+intros Hphi Hpsi.
+Hyp Hpsi.
+Qed.
+
+Ltac E_et_d' :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th _ P)
+  end.
+
+Ltac E_et_d phi :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th phi P)
+  end.
+
+Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
+intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
+elim Hphi_ou_psi.
+Hyp Hphi_imp_chi.
+Hyp Hpsi_imp_chi.
+Qed.
+
+Ltac E_ou' :=
+  match goal with
+  | |- ?P => eapply (E_ou_th _ _ P)
+  end.
+
+Ltac E_ou phi psi :=
+  match goal with
+  | |- ?P => apply (E_ou_th phi psi P)
+  end.
+
+Ltac I_ou_g :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_introl A B)
+  | _             => fail
+  end.
+
+Ltac I_ou_d :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_intror A B)
+  | _             => fail
+  end.
+
+Ltac I_exists' :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
+  | _                           => fail
+  end.
+
+Ltac I_exists t :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
+  | _                           => fail
+  end.
+
+Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
+Proof.
+firstorder.
+Qed.
+(*
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P)
+  end.
+*)
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
+  end.
+
+Ltac TE :=
+  unfold not;
+  match goal with
+  | |- (?P \/ (?P -> False)) => exact (classic P)
+  | _                        => fail
+  end.
+
+Theorem E_antiT_th : forall (phi : Prop), False -> phi.
+intros Pphi F.
+elim F.
+Qed.
+
+Ltac E_antiT :=
+  match goal with
+  | |- ?P => apply (E_antiT_th P)
+  end.
+
+Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
+unfold not.
+intro Pphi.
+intros Hphi Hnphi.
+cut Pphi.
+Hyp Hnphi.
+Hyp Hphi.
+Qed.
+
+Ltac I_antiT phi :=
+ match goal with
+ | |- False => apply (I_antiT_th phi)
+ end.
+
+Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
+intros.
+unfold not.
+exact H.
+Qed.
+
+Ltac I_non Nom :=
+ match goal with
+ | |- ~ ?P => apply (I_non_th P); intro Nom
+ end.
+
+Ltac E_non phi :=
+ apply (I_antiT_th phi).
+
+Ltac absurde Nom :=
+ match goal with
+ | |- ?P => apply (NNPP P); intro Nom
+ end.
+
+(*
+Ltac I_antiT phi := apply (I_antiT_th phi).
+
+Ltac absurde Nom phi :=
+match goal with
+| |- phi =>
+cut (phi \/ ~phi);
+[
+intros L;
+elim L;
+[
+auto
+|
+clear L;
+intro Nom;
+apply (E_antiT_th)
+]
+|
+apply (classic phi)
+]
+| _ => fail
+end.
+*)
+
diff --git a/TP1/TP1.v b/TP1/TP1.v
new file mode 100755
index 0000000..731bbef
--- /dev/null
+++ b/TP1/TP1.v
@@ -0,0 +1,119 @@
+(* Les règles de la déduction naturelle doivent être ajoutées à Coq. *)
+Require Import Naturelle.
+
+(* Ouverture d\u2019une section *)
+Section CalculPropositionnel.
+
+(* Déclaration de variables propositionnelles *)
+Variable A B C E Y R : Prop.
+
+(*Exerice 1*)
+
+Theorem Thm00 : A /\ B -> B /\ A.
+I_imp H.
+I_et.
+E_et_d A.
+Hyp H.
+E_et_g B.
+Hyp H.
+Qed.
+
+Theorem Thm_1 : ((A \/ B) -> C) -> (B -> C).
+I_imp H.
+I_imp H2.
+E_imp (A \/ B).
+Hyp H.
+I_ou_d.
+Hyp H2.
+Qed.
+
+Theorem Thm_2 : A -> ~~A.
+I_imp H.
+I_non H2.
+I_antiT A.
+Hyp H.
+Hyp H2.
+Qed.
+
+Theorem Thm_3 : (A -> B) -> (~B -> ~A).
+I_imp H.
+I_imp H2.
+I_non H3.
+I_antiT B.
+E_imp A.
+Hyp H.
+Hyp H3.
+Hyp H2.
+Qed.
+
+Theorem Thm_4 : ~~A -> A.
+I_imp H.
+absurde H2.
+I_antiT (~A).
+Hyp H2.
+Hyp H.
+Qed.
+
+Theorem Thm_5 : (~B -> ~A) -> (A -> B).
+
+I_imp H.
+I_imp H2.
+absurde H3.
+I_antiT (A).
+Hyp H2.
+E_imp (~B).
+trivial.
+trivial.
+Qed.
+
+Theorem Thm_6 : ((E -> (Y \/ R)) /\ (Y -> R)) -> (~R -> ~E).
+intros.
+I_non H1.
+I_antiT (R).
+E_ou Y R.
+E_imp E.
+E_et_g (Y -> R).
+Hyp H.
+Hyp H1.
+E_et_d (E -> Y \/ R).
+Hyp H.
+I_imp H2.
+tauto.
+tauto.
+Qed.
+
+(*Exerice 2*)
+
+Theorem Coq_E_imp : ((A -> B) /\ A) -> B.
+intros.
+destruct H as (H1,H2).
+tauto.
+Qed.
+
+Theorem Coq_E_et_g : (A /\ B) -> A.
+intros.
+destruct H as (H1,H2).
+trivial.
+Qed.
+
+Theorem Coq_E_ou : ((A \/ B) /\ (A -> C) /\ (B -> C)) -> C.
+intros.
+destruct H as (H1,H2).
+destruct H2 as (H2,H3).
+destruct H1 as [H4 | H5].
+E_imp A.
+Hyp H2.
+Hyp H4.
+E_imp B.
+trivial.
+trivial.
+Qed.
+
+Theorem Thm_7 : ((E -> (Y \/ R)) /\ (Y -> R)) -> (~R -> ~E).
+intros.
+destruct H as (H1,H2).
+tauto. (* à détailler *)
+Qed. 
+
+End CalculPropositionnel.
+
diff --git a/TP2-3/TP2-enigme.mlw b/TP2-3/TP2-enigme.mlw
new file mode 100644
index 0000000..c557982
--- /dev/null
+++ b/TP2-3/TP2-enigme.mlw
@@ -0,0 +1,29 @@
+theory Enigme
+
+  predicate a
+  predicate b
+  predicate c
+   
+  predicate da = b /\ (not c)
+  predicate db = a -> c
+  predicate dc = (not c) /\ ( a \/ b )
+  
+  goal Q1: not (da /\ db /\ dc)
+  (* on demande ensuite un contre exemple *)  
+  
+  goal Q2c: da /\ db -> dc         (* vrai *)
+  goal Q2b: dc /\ da -> db         (* faux *)
+  goal Q2a: db /\ dc -> da         (* vrai *)
+  
+  goal Q3a: (not a) /\ (not b) /\ (not c) -> da   (* faux, a ment *)
+  goal Q3b: (not a) /\ (not b) /\ (not c) -> db   (* b dit la vérité *)
+  goal Q3c: (not a) /\ (not b) /\ (not c) -> dc   (* faux, c ment *)
+  
+  goal Q4a: da /\ db /\ dc -> a                   (* faux, a innocent *)
+  goal Q4b: da /\ db /\ dc -> b                   (* b coupable *)
+  goal Q4c: da /\ db /\ dc -> c                   (* faux, c innocent *)
+  
+  goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
+  (* on demande ensuite un contre exemple *)
+
+end
diff --git a/TP2-3/TP2.v b/TP2-3/TP2.v
new file mode 100644
index 0000000..3a8ef43
--- /dev/null
+++ b/TP2-3/TP2.v
@@ -0,0 +1,45 @@
+(* Ouverture d’une section *)
+Section CalculPredicats.
+(* Définition de 2 domaines pour les prédicats *)
+Variable A B : Type.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_8 : forall (P Q : A -> Prop),
+               (forall x1 : A, (P x1) /\ (Q x1))
+            -> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
+intros.
+split.
+intro x2.
+destruct (H x2).
+exact H0.
+intro x3.
+destruct (H x3).
+exact H1.
+Qed.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_9 : forall (P : A -> B -> Prop),
+               (exists x1 : A, forall y1 : B, (P x1 y1))
+            ->  forall y2 : B, exists x2 : A, (P x2 y2).
+intros.
+destruct H.
+exists x.
+generalize y2.
+exact H.
+Qed.
+
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_10 : forall (P Q : A -> Prop),
+                (exists x1 : A, (P x1) -> (Q x1))
+             -> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
+intros.
+destruct H.
+exists x.
+cut (P x).
+exact H.
+generalize x.
+exact H0.
+Qed.
+
+End CalculPredicats.
\ No newline at end of file
diff --git a/TP2-3/TP2.v.crashcoqide b/TP2-3/TP2.v.crashcoqide
new file mode 100644
index 0000000..5aaba17
--- /dev/null
+++ b/TP2-3/TP2.v.crashcoqide
@@ -0,0 +1,49 @@
+(* Ouverture d’une section *)
+Section CalculPredicats.
+(* Définition de 2 domaines pour les prédicats *)
+Variable A B : Type.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_8 : forall (P Q : A -> Prop),
+               (forall x1 : A, (P x1) /\ (Q x1))
+            -> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
+intros.
+split.
+intro x2.
+exists.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+(* Formule du second ordre : Quantification des prédicats phi et psi 
+Theorem Thm_9 : forall (P : A -> B -> Prop),
+               (exists x1 : A, forall y1 : B, (P x1 y1))
+            ->  forall y2 : B, exists x2 : A, (P x2 y2).
+intros.*)
+
+(* Formule du second ordre : Quantification des prédicats phi et psi
+Theorem Thm_10 : forall (P Q : A -> Prop),
+                (exists x1 : A, (P x1) -> (Q x1))
+             -> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
+intros.
+exists x2.*)
+
+End CalculPredicats.
\ No newline at end of file
diff --git a/TP2-3/enigme.mlw b/TP2-3/enigme.mlw
new file mode 100644
index 0000000..c557982
--- /dev/null
+++ b/TP2-3/enigme.mlw
@@ -0,0 +1,29 @@
+theory Enigme
+
+  predicate a
+  predicate b
+  predicate c
+   
+  predicate da = b /\ (not c)
+  predicate db = a -> c
+  predicate dc = (not c) /\ ( a \/ b )
+  
+  goal Q1: not (da /\ db /\ dc)
+  (* on demande ensuite un contre exemple *)  
+  
+  goal Q2c: da /\ db -> dc         (* vrai *)
+  goal Q2b: dc /\ da -> db         (* faux *)
+  goal Q2a: db /\ dc -> da         (* vrai *)
+  
+  goal Q3a: (not a) /\ (not b) /\ (not c) -> da   (* faux, a ment *)
+  goal Q3b: (not a) /\ (not b) /\ (not c) -> db   (* b dit la vérité *)
+  goal Q3c: (not a) /\ (not b) /\ (not c) -> dc   (* faux, c ment *)
+  
+  goal Q4a: da /\ db /\ dc -> a                   (* faux, a innocent *)
+  goal Q4b: da /\ db /\ dc -> b                   (* b coupable *)
+  goal Q4c: da /\ db /\ dc -> c                   (* faux, c innocent *)
+  
+  goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
+  (* on demande ensuite un contre exemple *)
+
+end
diff --git a/TP2-3/enigme/enigme-Predicats-Thm01_1.cvc b/TP2-3/enigme/enigme-Predicats-Thm01_1.cvc
new file mode 100644
index 0000000..a91fa97
--- /dev/null
+++ b/TP2-3/enigme/enigme-Predicats-Thm01_1.cvc
@@ -0,0 +1,83 @@
+%%% this is a prelude for CVC3 
+uni : TYPE;
+
+ty : TYPE;
+
+sort: (ty, uni) -> BOOLEAN;
+
+witness: (ty) -> uni;
+
+% witness_sort
+  ASSERT (FORALL (a : ty): (sort(a, witness(a))));
+
+int: ty;
+
+real: ty;
+
+bool: ty;
+
+match_bool: (ty, BITVECTOR(1), uni, uni) -> uni;
+
+% match_bool_sort
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (x : BITVECTOR(1), x1 : uni, x2 : uni): (sort(a, match_bool(a, x,
+  x1, x2)))));
+
+% match_bool_True
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (z : uni, z1 : uni):
+  ((sort(a, z)) => (match_bool(a, 0bin1, z, z1) = z))));
+
+% match_bool_False
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (z : uni, z1 : uni):
+  ((sort(a, z1)) => (match_bool(a, 0bin0, z, z1) = z1))));
+
+index_bool: (BITVECTOR(1)) -> INT;
+
+% index_bool_True
+  ASSERT (index_bool(0bin1) = 0);
+
+% index_bool_False
+  ASSERT (index_bool(0bin0) = 1);
+
+% bool_inversion
+  ASSERT (FORALL (u : BITVECTOR(1)): ((u = 0bin1) OR (u = 0bin0)));
+
+tuple0 : TYPE;
+
+tuple01: ty;
+
+Tuple0: tuple0;
+
+% tuple0_inversion
+  ASSERT (FORALL (u : tuple0): (u = Tuple0));
+
+a: BOOLEAN;
+
+b: BOOLEAN;
+
+c: BOOLEAN;
+
+da: BOOLEAN;
+
+% da_def
+  ASSERT (da <=> (b AND (NOT c)));
+
+db: BOOLEAN;
+
+% db_def
+  ASSERT (db <=> (a => c));
+
+dc: BOOLEAN;
+
+% dc_def
+  ASSERT (dc <=> ((NOT c) AND (a OR b)));
+
+QUERY
+% Thm01
+ % File "enigme.mlw", line 13, characters 7-12
+  (da AND (db AND dc));
diff --git a/TP2-3/enigme/enigme-Predicats-Thm01_1.smt2 b/TP2-3/enigme/enigme-Predicats-Thm01_1.smt2
new file mode 100644
index 0000000..d170dce
--- /dev/null
+++ b/TP2-3/enigme/enigme-Predicats-Thm01_1.smt2
@@ -0,0 +1,29 @@
+;;; generated by SMT-LIB2 driver
+;;; SMT-LIB2 driver: bit-vectors, common part
+(declare-datatypes () ((tuple0 (Tuple0))))
+(declare-fun a () Bool)
+
+(declare-fun b () Bool)
+
+(declare-fun c () Bool)
+
+(declare-fun da () Bool)
+
+;; da_def
+  (assert (= da (and b (not c))))
+
+(declare-fun db () Bool)
+
+;; db_def
+  (assert (= db (=> a c)))
+
+(declare-fun dc () Bool)
+
+;; dc_def
+  (assert (= dc (and (not c) (or a b))))
+
+(assert
+;; Thm01
+ ;; File "enigme.mlw", line 13, characters 7-12
+  (not (and da (and db dc))))
+(check-sat)
diff --git a/TP2-3/enigme/enigme-Proposition-Q1_1.smt2 b/TP2-3/enigme/enigme-Proposition-Q1_1.smt2
new file mode 100644
index 0000000..baa492f
--- /dev/null
+++ b/TP2-3/enigme/enigme-Proposition-Q1_1.smt2
@@ -0,0 +1,34 @@
+;;; generated by SMT-LIB2 driver
+;;; SMT-LIB2 driver: bit-vectors, common part
+(declare-datatypes () ((tuple0 (Tuple0))))
+(declare-fun a () Bool)
+
+(declare-fun b () Bool)
+
+(declare-fun c () Bool)
+
+(declare-fun da () Bool)
+
+;; da_def
+  (assert (= da (and b (not c))))
+
+(declare-fun db () Bool)
+
+;; db_def
+  (assert (= db (=> a c)))
+
+(declare-fun dc () Bool)
+
+;; dc_def
+  (assert (= dc (and (not c) (or a b))))
+
+(declare-fun compat () Bool)
+
+;; compat_def
+  (assert (= compat (and da (and db dc))))
+
+(assert
+;; Q1
+ ;; File "enigme/../enigme.mlw", line 15, characters 7-9
+  (not (not compat)))
+(check-sat)
diff --git a/TP2-3/enigme/enigme_Predicats_Thm01_1.v b/TP2-3/enigme/enigme_Predicats_Thm01_1.v
new file mode 100644
index 0000000..da62a14
--- /dev/null
+++ b/TP2-3/enigme/enigme_Predicats_Thm01_1.v
@@ -0,0 +1,27 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+
+Parameter a: Prop.
+
+Parameter b: Prop.
+
+Parameter c: Prop.
+
+(* Why3 assumption *)
+Definition da : Prop := b /\ ~ c.
+
+(* Why3 assumption *)
+Definition db : Prop := a -> c.
+
+(* Why3 assumption *)
+Definition dc : Prop := ~ c /\ (a \/ b).
+
+(* Why3 goal *)
+Theorem Thm01 : da /\ (db /\ dc).
+Proof.
+
+
+Qed.
+
diff --git a/TP2-3/enigme/why3session.xml b/TP2-3/enigme/why3session.xml
new file mode 100644
index 0000000..683e08b
--- /dev/null
+++ b/TP2-3/enigme/why3session.xml
@@ -0,0 +1,46 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Z3" version="4.4.1" alternative="counterexamples" timelimit="5" steplimit="0" memlimit="1000"/>
+<file>
+<path name=".."/>
+<path name="enigme.mlw"/>
+<theory name="Enigme">
+ <goal name="Q1">
+ <proof prover="1"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2c" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2b">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2a" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3a">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3b" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3c">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4a">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4b" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4c">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q5">
+ <proof prover="1"><result status="unknown" time="0.00"/></proof>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP2-3/sujet.pdf b/TP2-3/sujet.pdf
new file mode 100644
index 0000000..22138a7
Binary files /dev/null and b/TP2-3/sujet.pdf differ
diff --git a/TP2/TP2.v b/TP2/TP2.v
new file mode 100755
index 0000000..3a8ef43
--- /dev/null
+++ b/TP2/TP2.v
@@ -0,0 +1,45 @@
+(* Ouverture d’une section *)
+Section CalculPredicats.
+(* Définition de 2 domaines pour les prédicats *)
+Variable A B : Type.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_8 : forall (P Q : A -> Prop),
+               (forall x1 : A, (P x1) /\ (Q x1))
+            -> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
+intros.
+split.
+intro x2.
+destruct (H x2).
+exact H0.
+intro x3.
+destruct (H x3).
+exact H1.
+Qed.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_9 : forall (P : A -> B -> Prop),
+               (exists x1 : A, forall y1 : B, (P x1 y1))
+            ->  forall y2 : B, exists x2 : A, (P x2 y2).
+intros.
+destruct H.
+exists x.
+generalize y2.
+exact H.
+Qed.
+
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_10 : forall (P Q : A -> Prop),
+                (exists x1 : A, (P x1) -> (Q x1))
+             -> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
+intros.
+destruct H.
+exists x.
+cut (P x).
+exact H.
+generalize x.
+exact H0.
+Qed.
+
+End CalculPredicats.
\ No newline at end of file
diff --git a/TP2/TP2.v.crashcoqide b/TP2/TP2.v.crashcoqide
new file mode 100755
index 0000000..5aaba17
--- /dev/null
+++ b/TP2/TP2.v.crashcoqide
@@ -0,0 +1,49 @@
+(* Ouverture d’une section *)
+Section CalculPredicats.
+(* Définition de 2 domaines pour les prédicats *)
+Variable A B : Type.
+
+(* Formule du second ordre : Quantification des prédicats phi et psi *)
+Theorem Thm_8 : forall (P Q : A -> Prop),
+               (forall x1 : A, (P x1) /\ (Q x1))
+            -> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
+intros.
+split.
+intro x2.
+exists.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+(* Formule du second ordre : Quantification des prédicats phi et psi 
+Theorem Thm_9 : forall (P : A -> B -> Prop),
+               (exists x1 : A, forall y1 : B, (P x1 y1))
+            ->  forall y2 : B, exists x2 : A, (P x2 y2).
+intros.*)
+
+(* Formule du second ordre : Quantification des prédicats phi et psi
+Theorem Thm_10 : forall (P Q : A -> Prop),
+                (exists x1 : A, (P x1) -> (Q x1))
+             -> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
+intros.
+exists x2.*)
+
+End CalculPredicats.
\ No newline at end of file
diff --git a/TP2/enigme.mlw b/TP2/enigme.mlw
new file mode 100755
index 0000000..c557982
--- /dev/null
+++ b/TP2/enigme.mlw
@@ -0,0 +1,29 @@
+theory Enigme
+
+  predicate a
+  predicate b
+  predicate c
+   
+  predicate da = b /\ (not c)
+  predicate db = a -> c
+  predicate dc = (not c) /\ ( a \/ b )
+  
+  goal Q1: not (da /\ db /\ dc)
+  (* on demande ensuite un contre exemple *)  
+  
+  goal Q2c: da /\ db -> dc         (* vrai *)
+  goal Q2b: dc /\ da -> db         (* faux *)
+  goal Q2a: db /\ dc -> da         (* vrai *)
+  
+  goal Q3a: (not a) /\ (not b) /\ (not c) -> da   (* faux, a ment *)
+  goal Q3b: (not a) /\ (not b) /\ (not c) -> db   (* b dit la vérité *)
+  goal Q3c: (not a) /\ (not b) /\ (not c) -> dc   (* faux, c ment *)
+  
+  goal Q4a: da /\ db /\ dc -> a                   (* faux, a innocent *)
+  goal Q4b: da /\ db /\ dc -> b                   (* b coupable *)
+  goal Q4c: da /\ db /\ dc -> c                   (* faux, c innocent *)
+  
+  goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
+  (* on demande ensuite un contre exemple *)
+
+end
diff --git a/TP2/enigme/enigme-Predicats-Thm01_1.cvc b/TP2/enigme/enigme-Predicats-Thm01_1.cvc
new file mode 100755
index 0000000..a91fa97
--- /dev/null
+++ b/TP2/enigme/enigme-Predicats-Thm01_1.cvc
@@ -0,0 +1,83 @@
+%%% this is a prelude for CVC3 
+uni : TYPE;
+
+ty : TYPE;
+
+sort: (ty, uni) -> BOOLEAN;
+
+witness: (ty) -> uni;
+
+% witness_sort
+  ASSERT (FORALL (a : ty): (sort(a, witness(a))));
+
+int: ty;
+
+real: ty;
+
+bool: ty;
+
+match_bool: (ty, BITVECTOR(1), uni, uni) -> uni;
+
+% match_bool_sort
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (x : BITVECTOR(1), x1 : uni, x2 : uni): (sort(a, match_bool(a, x,
+  x1, x2)))));
+
+% match_bool_True
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (z : uni, z1 : uni):
+  ((sort(a, z)) => (match_bool(a, 0bin1, z, z1) = z))));
+
+% match_bool_False
+  ASSERT
+  (FORALL (a : ty):
+  (FORALL (z : uni, z1 : uni):
+  ((sort(a, z1)) => (match_bool(a, 0bin0, z, z1) = z1))));
+
+index_bool: (BITVECTOR(1)) -> INT;
+
+% index_bool_True
+  ASSERT (index_bool(0bin1) = 0);
+
+% index_bool_False
+  ASSERT (index_bool(0bin0) = 1);
+
+% bool_inversion
+  ASSERT (FORALL (u : BITVECTOR(1)): ((u = 0bin1) OR (u = 0bin0)));
+
+tuple0 : TYPE;
+
+tuple01: ty;
+
+Tuple0: tuple0;
+
+% tuple0_inversion
+  ASSERT (FORALL (u : tuple0): (u = Tuple0));
+
+a: BOOLEAN;
+
+b: BOOLEAN;
+
+c: BOOLEAN;
+
+da: BOOLEAN;
+
+% da_def
+  ASSERT (da <=> (b AND (NOT c)));
+
+db: BOOLEAN;
+
+% db_def
+  ASSERT (db <=> (a => c));
+
+dc: BOOLEAN;
+
+% dc_def
+  ASSERT (dc <=> ((NOT c) AND (a OR b)));
+
+QUERY
+% Thm01
+ % File "enigme.mlw", line 13, characters 7-12
+  (da AND (db AND dc));
diff --git a/TP2/enigme/enigme-Predicats-Thm01_1.smt2 b/TP2/enigme/enigme-Predicats-Thm01_1.smt2
new file mode 100755
index 0000000..d170dce
--- /dev/null
+++ b/TP2/enigme/enigme-Predicats-Thm01_1.smt2
@@ -0,0 +1,29 @@
+;;; generated by SMT-LIB2 driver
+;;; SMT-LIB2 driver: bit-vectors, common part
+(declare-datatypes () ((tuple0 (Tuple0))))
+(declare-fun a () Bool)
+
+(declare-fun b () Bool)
+
+(declare-fun c () Bool)
+
+(declare-fun da () Bool)
+
+;; da_def
+  (assert (= da (and b (not c))))
+
+(declare-fun db () Bool)
+
+;; db_def
+  (assert (= db (=> a c)))
+
+(declare-fun dc () Bool)
+
+;; dc_def
+  (assert (= dc (and (not c) (or a b))))
+
+(assert
+;; Thm01
+ ;; File "enigme.mlw", line 13, characters 7-12
+  (not (and da (and db dc))))
+(check-sat)
diff --git a/TP2/enigme/enigme-Proposition-Q1_1.smt2 b/TP2/enigme/enigme-Proposition-Q1_1.smt2
new file mode 100755
index 0000000..baa492f
--- /dev/null
+++ b/TP2/enigme/enigme-Proposition-Q1_1.smt2
@@ -0,0 +1,34 @@
+;;; generated by SMT-LIB2 driver
+;;; SMT-LIB2 driver: bit-vectors, common part
+(declare-datatypes () ((tuple0 (Tuple0))))
+(declare-fun a () Bool)
+
+(declare-fun b () Bool)
+
+(declare-fun c () Bool)
+
+(declare-fun da () Bool)
+
+;; da_def
+  (assert (= da (and b (not c))))
+
+(declare-fun db () Bool)
+
+;; db_def
+  (assert (= db (=> a c)))
+
+(declare-fun dc () Bool)
+
+;; dc_def
+  (assert (= dc (and (not c) (or a b))))
+
+(declare-fun compat () Bool)
+
+;; compat_def
+  (assert (= compat (and da (and db dc))))
+
+(assert
+;; Q1
+ ;; File "enigme/../enigme.mlw", line 15, characters 7-9
+  (not (not compat)))
+(check-sat)
diff --git a/TP2/enigme/enigme_Predicats_Thm01_1.v b/TP2/enigme/enigme_Predicats_Thm01_1.v
new file mode 100755
index 0000000..da62a14
--- /dev/null
+++ b/TP2/enigme/enigme_Predicats_Thm01_1.v
@@ -0,0 +1,27 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+
+Parameter a: Prop.
+
+Parameter b: Prop.
+
+Parameter c: Prop.
+
+(* Why3 assumption *)
+Definition da : Prop := b /\ ~ c.
+
+(* Why3 assumption *)
+Definition db : Prop := a -> c.
+
+(* Why3 assumption *)
+Definition dc : Prop := ~ c /\ (a \/ b).
+
+(* Why3 goal *)
+Theorem Thm01 : da /\ (db /\ dc).
+Proof.
+
+
+Qed.
+
diff --git a/TP2/enigme/why3session.xml b/TP2/enigme/why3session.xml
new file mode 100755
index 0000000..683e08b
--- /dev/null
+++ b/TP2/enigme/why3session.xml
@@ -0,0 +1,46 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Z3" version="4.4.1" alternative="counterexamples" timelimit="5" steplimit="0" memlimit="1000"/>
+<file>
+<path name=".."/>
+<path name="enigme.mlw"/>
+<theory name="Enigme">
+ <goal name="Q1">
+ <proof prover="1"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2c" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2b">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q2a" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3a">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3b" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q3c">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4a">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4b" proved="true">
+ <proof prover="0"><result status="valid" time="0.00"/></proof>
+ </goal>
+ <goal name="Q4c">
+ <proof prover="0"><result status="unknown" time="0.00"/></proof>
+ </goal>
+ <goal name="Q5">
+ <proof prover="1"><result status="unknown" time="0.00"/></proof>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP4/induction-etu.mlw b/TP4/induction-etu.mlw
new file mode 100644
index 0000000..7970ca3
--- /dev/null
+++ b/TP4/induction-etu.mlw
@@ -0,0 +1,23 @@
+theory Induction
+
+(* Définition du type inductif liste *)
+type liste 'a = Nil | Cons 'a (liste 'a)
+
+(* Concaténation de deux listes *)
+function append (l1 l2 : liste 'a) : liste 'a =
+   match l1 with
+      | Nil -> l2
+      | Cons t q -> Cons t (append q l2)
+   end
+
+lemma append_Nil_left : forall l : liste 'a. append Nil l = l
+
+lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
+   append (Cons e l1) l2 = Cons e (append l1 l2)
+
+lemma append_Nil_right: forall l : liste 'a. append l Nil = l
+
+lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
+   append l1 (append l2 l3) = append (append l1 l2) l3
+
+end
\ No newline at end of file
diff --git a/TP4/induction-etu.v b/TP4/induction-etu.v
new file mode 100644
index 0000000..954c5a4
--- /dev/null
+++ b/TP4/induction-etu.v
@@ -0,0 +1,121 @@
+Require Import Extraction.
+(* Ouverture d’une section *)
+Section Induction.
+(* Déclaration d’un domaine pour les éléments des listes *)
+Variable A : Set.
+
+Inductive liste : Set :=
+  Nil : liste
+| Cons : A -> liste -> liste.
+
+(* Déclaration du nom de la fonction *)
+Variable append_spec : liste -> liste -> liste.
+
+(* Spécification du comportement pour Nil *)
+Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
+
+(* Spécification du comportement pour Cons *)
+Axiom append_Cons : forall (t : A), forall (q l : liste),
+   append_spec (Cons t q) l = Cons t (append_spec q l).
+
+Theorem append_Nil_right : forall (l : liste), (append_spec l Nil) = l.
+intros.
+induction l.
+(*cas de base*)
+apply append_Nil.
+(*cas general*)
+rewrite append_Cons.
+rewrite IHl.
+reflexivity.
+Qed.
+
+Theorem append_associative : forall (l1 l2 l3 : liste),
+   (append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
+intros.
+induction l1.
+(*cas de base*)
+rewrite append_Nil.
+rewrite append_Nil.
+reflexivity.
+(*cas general*)
+rewrite append_Cons.
+rewrite IHl1.
+rewrite append_Cons.
+rewrite append_Cons.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction append *)
+Fixpoint append_impl (l1 l2 : liste) {struct l1} : liste :=
+   match l1 with
+      Nil => l2
+      | (Cons t1 q1) => (Cons t1 (append_impl q1 l2))
+end.
+
+Theorem append_correctness : forall (l1 l2 : liste),
+   (append_spec l1 l2) = (append_impl l1 l2).
+intros.
+induction l1.
+(*cas de base*)
+rewrite append_Nil.
+simpl append_impl.
+reflexivity.
+(*cas general*)
+rewrite append_Cons.
+simpl append_impl.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction rev (reverse d'une liste) *)
+Fixpoint rev_impl (l : liste) : liste :=
+   match l with
+    Nil => Nil
+    | (Cons t1 q1) => (append_impl (rev_impl q1)( Cons t1 Nil))
+end.
+
+Lemma rev_append : forall (l1 l2 : liste),
+   (rev_impl (append_impl l1 l2)) = (append_impl (rev_impl l2) (rev_impl l1)).
+intros.
+induction l1.
+(*cas de base *)
+simpl append_impl.
+rewrite <- append_correctness.
+rewrite append_Nil_right.
+reflexivity.
+(*cas general*)
+simpl rev_impl.
+rewrite IHl1.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite append_associative.
+reflexivity.
+Qed.
+
+Theorem rev_rev : forall (l : liste), (rev_impl (rev_impl l)) = l.
+intros.
+induction l.
+(*Cas de base*)
+simpl rev_impl.
+reflexivity.
+(*cas general*)
+simpl rev_impl.
+rewrite rev_append.
+rewrite IHl.
+simpl rev_impl.
+rewrite <- append_correctness.
+rewrite append_Cons.
+rewrite append_Nil.
+reflexivity.
+Qed.
+
+End Induction.
+
+Extraction Language Ocaml.
+Extraction "/tmp/induction" append_impl rev_impl.
+Extraction Language Haskell.
+Extraction "/tmp/induction" append_impl rev_impl.
+Extraction Language Scheme.
+Extraction "/tmp/induction" append_impl rev_impl.
diff --git a/TP4/readme.txt b/TP4/readme.txt
new file mode 100644
index 0000000..b626354
--- /dev/null
+++ b/TP4/readme.txt
@@ -0,0 +1,9 @@
+2020-10-13
+Modélisation TP4
+http://moodle-n7.inp-toulouse.fr/pluginfile.php/90409/mod_resource/content/4/equipes-TD5TD6.txt
+
+Membres de groupe G-5:
+EL HADFI Younes
+HAMMAMI Linda
+HAUTEVILLE Leane
+FAINSIN Laurent
diff --git a/TP5/induction-etu.mlw b/TP5/induction-etu.mlw
new file mode 100755
index 0000000..7970ca3
--- /dev/null
+++ b/TP5/induction-etu.mlw
@@ -0,0 +1,23 @@
+theory Induction
+
+(* Définition du type inductif liste *)
+type liste 'a = Nil | Cons 'a (liste 'a)
+
+(* Concaténation de deux listes *)
+function append (l1 l2 : liste 'a) : liste 'a =
+   match l1 with
+      | Nil -> l2
+      | Cons t q -> Cons t (append q l2)
+   end
+
+lemma append_Nil_left : forall l : liste 'a. append Nil l = l
+
+lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
+   append (Cons e l1) l2 = Cons e (append l1 l2)
+
+lemma append_Nil_right: forall l : liste 'a. append l Nil = l
+
+lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
+   append l1 (append l2 l3) = append (append l1 l2) l3
+
+end
\ No newline at end of file
diff --git a/TP5/induction-etu.v b/TP5/induction-etu.v
new file mode 100755
index 0000000..d93cb9f
--- /dev/null
+++ b/TP5/induction-etu.v
@@ -0,0 +1,123 @@
+Require Import Extraction.
+(* Ouverture d’une section *)
+Section Induction.
+(* Déclaration d’un domaine pour les éléments des listes *)
+Variable A : Set.
+
+Inductive liste : Set :=
+  Nil : liste
+| Cons : A -> liste -> liste.
+
+(* Déclaration du nom de la fonction *)
+Variable append_spec : liste -> liste -> liste.
+
+(* Spécification du comportement pour Nil *)
+Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
+
+(* Spécification du comportement pour Cons *)
+Axiom append_Cons : forall (t : A), forall (q l : liste),
+   append_spec (Cons t q) l = Cons t (append_spec q l).
+
+Theorem append_Nil_right : forall (l : liste), (append_spec l Nil) = l.
+intros.
+induction l.
+(* cas de base *)
+apply append_Nil.
+(* cas général *)
+rewrite append_Cons.
+rewrite IHl.
+reflexivity.
+Qed.
+
+
+Theorem append_associative : forall (l1 l2 l3 : liste),
+   (append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
+intros.
+induction l1.
+(* cas de base *)
+rewrite append_Nil.
+rewrite append_Nil.
+reflexivity.
+(* cas général *)
+rewrite append_Cons.
+rewrite append_Cons.
+rewrite append_Cons.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+
+(* Implantation de la fonction append *)
+Fixpoint append_impl (l1 l2 : liste) {struct l1} : liste :=
+   match l1 with
+      Nil => l2
+      | (Cons t1 q1) => (Cons t1 (append_impl q1 l2))
+end.
+
+Theorem append_correctness : forall (l1 l2 : liste),
+   (append_spec l1 l2) = (append_impl l1 l2).
+intros.
+induction l1.
+(* cas de base *)
+rewrite append_Nil.
+simpl append_impl.
+reflexivity.
+(* cas général *)
+rewrite append_Cons.
+simpl append_impl.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction rev (reverse d'une liste) *)
+Fixpoint rev_impl (l : liste) : liste :=
+   match l with
+    Nil => l
+    | (Cons x y) => ( append_impl (rev_impl y) (Cons x Nil) )
+end.
+
+
+Lemma rev_append : forall (l1 l2 : liste),
+   (rev_impl (append_impl l1 l2)) = (append_impl (rev_impl l2) (rev_impl l1)).
+intros.
+induction l1.
+(* cas de base *)
+simpl rev_impl.
+rewrite <- append_correctness.
+rewrite append_Nil_right.
+reflexivity.
+(* cas général *)
+simpl rev_impl.
+rewrite IHl1.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite <- append_correctness.
+rewrite append_associative.
+reflexivity.
+Qed.
+
+Theorem rev_rev : forall (l : liste), (rev_impl (rev_impl l)) = l.
+intros.
+induction l.
+(* cas de base *)
+simpl rev_impl.
+reflexivity.
+(* cas général *)
+simpl rev_impl.
+rewrite rev_append.
+rewrite IHl.
+simpl rev_impl.
+rewrite <- append_correctness.
+rewrite append_Cons.
+rewrite append_Nil.
+reflexivity.
+Qed.
+
+End Induction.
+Extraction Language Ocaml.
+Extraction "/tmp/induction" append_impl rev_impl.
+Extraction Language Haskell.
+Extraction "/tmp/induction" append_impl rev_impl.
+Extraction Language Scheme.
+Extraction "/tmp/induction" append_impl rev_impl.
diff --git a/TP5/induction-etu.wlm b/TP5/induction-etu.wlm
new file mode 100755
index 0000000..7970ca3
--- /dev/null
+++ b/TP5/induction-etu.wlm
@@ -0,0 +1,23 @@
+theory Induction
+
+(* Définition du type inductif liste *)
+type liste 'a = Nil | Cons 'a (liste 'a)
+
+(* Concaténation de deux listes *)
+function append (l1 l2 : liste 'a) : liste 'a =
+   match l1 with
+      | Nil -> l2
+      | Cons t q -> Cons t (append q l2)
+   end
+
+lemma append_Nil_left : forall l : liste 'a. append Nil l = l
+
+lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
+   append (Cons e l1) l2 = Cons e (append l1 l2)
+
+lemma append_Nil_right: forall l : liste 'a. append l Nil = l
+
+lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
+   append l1 (append l2 l3) = append (append l1 l2) l3
+
+end
\ No newline at end of file
diff --git a/TP5/induction-etu/why3session.xml b/TP5/induction-etu/why3session.xml
new file mode 100755
index 0000000..a0ad9c4
--- /dev/null
+++ b/TP5/induction-etu/why3session.xml
@@ -0,0 +1,32 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="induction-etu.mlw"/>
+<theory name="Induction" proved="true">
+ <goal name="append_Nil_left" proved="true">
+ <proof prover="0"><result status="valid" time="0.01"/></proof>
+ </goal>
+ <goal name="append_Cons_left" proved="true">
+ <proof prover="0"><result status="valid" time="0.01"/></proof>
+ </goal>
+ <goal name="append_Nil_right" proved="true">
+ <transf name="induction_ty_lex" proved="true" >
+  <goal name="append_Nil_right.0" proved="true">
+  <proof prover="0"><result status="valid" time="0.00"/></proof>
+  </goal>
+ </transf>
+ </goal>
+ <goal name="append_associative" proved="true">
+ <transf name="induction_ty_lex" proved="true" >
+  <goal name="append_associative.0" proved="true">
+  <proof prover="0"><result status="valid" time="0.01"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP6/ascendant.mlw b/TP6/ascendant.mlw
new file mode 100755
index 0000000..8666063
--- /dev/null
+++ b/TP6/ascendant.mlw
@@ -0,0 +1,37 @@
+(* Spécification de la fonction factorielle *)
+
+theory Factorielle
+
+   use int.Int
+
+   function factorielle( n : int ) : int
+
+   axiom factorielle_zero : (factorielle zero) = one
+
+   axiom factorielle_succ : forall n : int. (n > 0) -> (factorielle n) = (n * (factorielle (n - 1)))
+
+end
+
+(* Implémentation de la fonction factorielle par un algorithme ascendant *)
+
+module FactorielleAscendant
+
+  use int.Int
+  use ref.Refint
+  use Factorielle
+
+  let factorielle_ascendant (n: int) : int
+    requires { 0 <= n }
+    ensures  { result = (factorielle n) }
+  =
+    let i = ref 0 in
+    let r = ref 1 in
+    while  (!i < n) do
+      invariant { !r = (factorielle !i) && ( 0 <= !i <= n ) }
+      variant   { n - !i }
+      i := (!i) + 1;
+      r := (!i) * (!r) 
+    done;
+    !r
+
+end
diff --git a/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v
new file mode 100755
index 0000000..2a3167a
--- /dev/null
+++ b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v
@@ -0,0 +1,42 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter factorielle: Z -> Z.
+
+Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
+
+Axiom factorielle_succ :
+  forall (n:Z), (0%Z < n)%Z ->
+  ((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
+
+Parameter n: Z.
+
+Axiom H : (0%Z <= n)%Z.
+
+(* Why3 goal *)
+Theorem VC_factorielle_ascendant :
+  (1%Z = (factorielle 0%Z)) /\ ((0%Z <= 0%Z)%Z /\ (0%Z <= n)%Z).
+split.
+rewrite factorielle_zero.
+reflexivity.
+split.
+omega.
+apply H.
+Qed.
+
diff --git a/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_2.v b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_2.v
new file mode 100755
index 0000000..ee12c35
--- /dev/null
+++ b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_2.v
@@ -0,0 +1,67 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter factorielle: Z -> Z.
+
+Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
+
+Axiom factorielle_succ :
+  forall (n:Z), (0%Z < n)%Z ->
+  ((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
+
+Parameter n: Z.
+
+Axiom H : (0%Z <= n)%Z.
+
+Parameter r: Z.
+
+Parameter i: Z.
+
+Axiom H1 : (r = (factorielle i)).
+
+Axiom H2 : (0%Z <= i)%Z.
+
+Axiom H3 : (i <= n)%Z.
+
+Axiom H4 : (i < n)%Z.
+
+Parameter i1: Z.
+
+Axiom H5 : (i1 = (i + 1%Z)%Z).
+
+Parameter r1: Z.
+
+Axiom H6 : (r1 = (i1 * r)%Z).
+
+(* Why3 goal *)
+Theorem VC_factorielle_ascendant :
+  (0%Z <= (n - i)%Z)%Z /\ ((n - i1)%Z < (n - i)%Z)%Z.
+split.
+generalize H.
+intros.
+generalize H3.
+intros.
+omega.
+generalize H.
+intros.
+generalize H5.
+intros.
+omega.
+Qed.
+
diff --git a/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_3.v b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_3.v
new file mode 100755
index 0000000..750c948
--- /dev/null
+++ b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_3.v
@@ -0,0 +1,70 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter factorielle: Z -> Z.
+
+Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
+
+Axiom factorielle_succ :
+  forall (n:Z), (0%Z < n)%Z ->
+  ((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
+
+Parameter n: Z.
+
+Axiom H : (0%Z <= n)%Z.
+
+Parameter r: Z.
+
+Parameter i: Z.
+
+Axiom H1 : (r = (factorielle i)).
+
+Axiom H2 : (0%Z <= i)%Z.
+
+Axiom H3 : (i <= n)%Z.
+
+Axiom H4 : (i < n)%Z.
+
+Parameter i1: Z.
+
+Axiom H5 : (i1 = (i + 1%Z)%Z).
+
+Parameter r1: Z.
+
+Axiom H6 : (r1 = (i1 * r)%Z).
+
+Axiom H7 : ((i+1-1) = i)%Z.
+
+(* Why3 goal *)
+Theorem VC_factorielle_ascendant :
+  (r1 = (factorielle i1)) /\ ((0%Z <= i1)%Z /\ (i1 <= n)%Z).
+split.
+generalize H1.
+intros.
+rewrite H6.
+rewrite -> factorielle_succ.
+rewrite H5.
+rewrite H0.
+rewrite H7.
+reflexivity.
+generalize H2.
+intros.
+rewrite H5.
+Qed.
+
diff --git a/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v
new file mode 100755
index 0000000..1165424
--- /dev/null
+++ b/TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v
@@ -0,0 +1,52 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+Require int.Int.
+
+(* Why3 assumption *)
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
+Existing Instance ref_WhyType.
+Arguments mk_ref {a}.
+
+(* Why3 assumption *)
+Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
+  match v with
+  | mk_ref x => x
+  end.
+
+Parameter factorielle: Z -> Z.
+
+Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
+
+Axiom factorielle_succ :
+  forall (n:Z), (0%Z < n)%Z ->
+  ((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
+
+Parameter n: Z.
+
+Axiom H : (0%Z <= n)%Z.
+
+Parameter r: Z.
+
+Parameter i: Z.
+
+Axiom H1 : (r = (factorielle i)).
+
+Axiom H2 : (0%Z <= i)%Z.
+
+Axiom H3 : (i <= n)%Z.
+Axiom H4 : ~ (i < n)%Z.
+
+(* H3 et H4 implique H43 *)
+Axiom H34 : ( i = n )%Z.
+
+(* Why3 goal *)
+Theorem VC_factorielle_ascendant : (r = (factorielle n)).
+rewrite H1.
+rewrite H34.
+reflexivity.
+Qed.
+
diff --git a/TP6/ascendant/why3session.xml b/TP6/ascendant/why3session.xml
new file mode 100755
index 0000000..bb94a95
--- /dev/null
+++ b/TP6/ascendant/why3session.xml
@@ -0,0 +1,45 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="Coq" version="8.9.1" timelimit="0" steplimit="0" memlimit="0"/>
+<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="5" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="ascendant.mlw"/>
+<theory name="FactorielleAscendant" proved="true">
+ <goal name="VC factorielle_ascendant" expl="VC for factorielle_ascendant" proved="true">
+ <transf name="split_vc" proved="true" >
+  <goal name="VC factorielle_ascendant.0" expl="loop invariant init" proved="true">
+  <proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v"><result status="valid" time="0.35"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
+  <proof prover="2"><result status="valid" time="0.00"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.00"/></proof>
+  <proof prover="5"><result status="valid" time="0.00"/></proof>
+  </goal>
+  <goal name="VC factorielle_ascendant.1" expl="loop variant decrease" proved="true">
+  <proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_2.v"><result status="unknown" time="0.33"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
+  </goal>
+  <goal name="VC factorielle_ascendant.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_3.v"><result status="unknown" time="0.30"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="10"/></proof>
+  <proof prover="2"><result status="valid" time="0.00"/></proof>
+  <proof prover="3"><result status="valid" time="0.05"/></proof>
+  <proof prover="4"><result status="valid" time="0.05"/></proof>
+  <proof prover="5"><result status="valid" time="0.00"/></proof>
+  </goal>
+  <goal name="VC factorielle_ascendant.3" expl="postcondition" proved="true">
+  <proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v"><result status="unknown" time="0.31"/></proof>
+  <proof prover="1"><result status="valid" time="0.00" steps="7"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP6/descendant.mlw b/TP6/descendant.mlw
new file mode 100755
index 0000000..4d7c0f2
--- /dev/null
+++ b/TP6/descendant.mlw
@@ -0,0 +1,37 @@
+(* Spécification de la fonction factorielle *)
+
+theory Factorielle
+
+   use int.Int
+
+   function factorielle( n : int ) : int
+
+   axiom factorielle_zero : (factorielle zero) = one
+
+   axiom factorielle_succ : forall n : int. (n > 0) -> (factorielle n) = (n * (factorielle (n - 1)))
+
+end
+
+(* Implémentation de la fonction factorielle par un algorithme descendant *)
+
+module FactorielleDescendant
+
+  use int.Int
+  use Factorielle
+  use ref.Refint
+
+  let factorielle_descendant (n: int) : int
+    requires { 0 <= n }
+    ensures  { result = (factorielle n) }
+  =
+    let i = ref n in
+    let r = ref 1 in
+    while  (0 < !i) do
+      invariant { !r * factorielle !i = factorielle n && 0 <= !i }
+      variant   { !i }
+      r := !i * !r;
+      i := !i - 1
+    done;
+    !r
+
+end
diff --git a/TP6/descendant/why3session.xml b/TP6/descendant/why3session.xml
new file mode 100755
index 0000000..dd7a418
--- /dev/null
+++ b/TP6/descendant/why3session.xml
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="descendant.mlw"/>
+<theory name="FactorielleDescendant" proved="true">
+ <goal name="VC factorielle_descendant" expl="VC for factorielle_descendant" proved="true">
+ <transf name="split_vc" proved="true" >
+  <goal name="VC factorielle_descendant.0" expl="loop invariant init" proved="true">
+  <proof prover="0"><result status="valid" time="0.00"/></proof>
+  <proof prover="1"><result status="valid" time="0.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="3"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.00"/></proof>
+  </goal>
+  <goal name="VC factorielle_descendant.1" expl="loop variant decrease" proved="true">
+  <proof prover="0"><result status="valid" time="0.00"/></proof>
+  <proof prover="1"><result status="valid" time="0.01"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="8"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.01"/></proof>
+  </goal>
+  <goal name="VC factorielle_descendant.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.01"/></proof>
+  <proof prover="1"><result status="timeout" time="5.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
+  <proof prover="3"><result status="timeout" time="5.00"/></proof>
+  <proof prover="4"><result status="failure" time="0.00"/></proof>
+  </goal>
+  <goal name="VC factorielle_descendant.3" expl="postcondition" proved="true">
+  <proof prover="0"><result status="valid" time="0.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="6"/></proof>
+  <proof prover="3"><result status="valid" time="0.00"/></proof>
+  <proof prover="4"><result status="failure" time="0.00"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP6/division.mlw b/TP6/division.mlw
new file mode 100755
index 0000000..418b256
--- /dev/null
+++ b/TP6/division.mlw
@@ -0,0 +1,23 @@
+
+(* Division entière par l'algorithme d'Euclide *)
+
+module Division
+
+  use int.Int
+  use ref.Refint
+
+  let division (a b: int) (* renvoie une paire d'entiers (quotient,reste) *)
+    requires { 0 <= a && 0 < b }
+    ensures  { let (q,r) = result in q * b + r = a && 0 <= r < b }
+  =
+    let q = ref 0 in
+    let r = ref a in
+    while !r >= b do
+      invariant { a = !q * b + !r && 0 <= !q && 0 <= !r }
+      variant   { !r - b }
+      q := (!q) + 1;
+      r := (!r) - b
+    done;
+    (!q,!r)
+
+end
diff --git a/TP6/division/why3session.xml b/TP6/division/why3session.xml
new file mode 100755
index 0000000..86c96fa
--- /dev/null
+++ b/TP6/division/why3session.xml
@@ -0,0 +1,28 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="division.mlw"/>
+<theory name="Division" proved="true">
+ <goal name="VC division" expl="VC for division" proved="true">
+ <transf name="split_vc" proved="true" >
+  <goal name="VC division.0" expl="loop invariant init" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
+  </goal>
+  <goal name="VC division.1" expl="loop variant decrease" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
+  </goal>
+  <goal name="VC division.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
+  </goal>
+  <goal name="VC division.3" expl="postcondition" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP6/pgcd.mlw b/TP6/pgcd.mlw
new file mode 100755
index 0000000..8a1d401
--- /dev/null
+++ b/TP6/pgcd.mlw
@@ -0,0 +1,38 @@
+
+(* PGCD : Algorithme Euclide *)
+
+theory PGCD
+
+  use int.Int
+
+  function pgcd(a b : int) : int
+
+  axiom A1 : forall a: int. (a>0) -> ( pgcd a a ) = a
+  axiom A2 : forall a,b: int. (a>0 && b>0) -> ( pgcd a b ) = ( pgcd b a )
+  axiom A3 : forall a,b: int. (a>b>0) -> ( pgcd a b ) = (pgcd (a-b) b )
+
+end
+
+module PGCDEuclide
+
+  use import int.Int
+  use import ref.Refint
+  use import PGCD
+
+  let pgcd_euclide (a b: int) : int
+    requires { 0 < a && 0 < b }
+    ensures  { result = (pgcd a b)}
+  =
+    let ap = ref a in
+    let bp = ref b in
+    while (!ap <> !bp) do
+      invariant { (pgcd a b ) = ( pgcd !ap !bp ) && !ap > 0 && !bp > 0 }
+      variant   { !ap + !bp }
+      if (!ap <= !bp) then
+      	 bp := !bp - !ap
+      else
+      	 ap := !ap - !bp
+    done;
+    !ap
+
+end
diff --git a/TP6/pgcd/why3session.xml b/TP6/pgcd/why3session.xml
new file mode 100755
index 0000000..92cf434
--- /dev/null
+++ b/TP6/pgcd/why3session.xml
@@ -0,0 +1,58 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="pgcd.mlw"/>
+<theory name="PGCDEuclide" proved="true">
+ <goal name="VC pgcd_euclide" expl="VC for pgcd_euclide" proved="true">
+ <transf name="split_vc" proved="true" >
+  <goal name="VC pgcd_euclide.0" expl="loop invariant init" proved="true">
+  <proof prover="2"><result status="valid" time="0.00" steps="3"/></proof>
+  </goal>
+  <goal name="VC pgcd_euclide.1" expl="loop variant decrease" proved="true">
+  <proof prover="0"><result status="valid" time="0.01"/></proof>
+  <proof prover="1"><result status="valid" time="0.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="9"/></proof>
+  <proof prover="3"><result status="valid" time="0.00"/></proof>
+  <proof prover="4"><result status="valid" time="0.00"/></proof>
+  </goal>
+  <goal name="VC pgcd_euclide.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.01"/></proof>
+  <proof prover="1"><result status="valid" time="0.02"/></proof>
+  <proof prover="2"><result status="valid" time="0.01" steps="21"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.01"/></proof>
+  </goal>
+  <goal name="VC pgcd_euclide.3" expl="loop variant decrease" proved="true">
+  <proof prover="0"><result status="valid" time="0.00"/></proof>
+  <proof prover="1"><result status="valid" time="0.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="9"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.00"/></proof>
+  </goal>
+  <goal name="VC pgcd_euclide.4" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.01"/></proof>
+  <proof prover="1"><result status="valid" time="0.01"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="14"/></proof>
+  <proof prover="3"><result status="valid" time="0.00"/></proof>
+  <proof prover="4"><result status="valid" time="0.01"/></proof>
+  </goal>
+  <goal name="VC pgcd_euclide.5" expl="postcondition" proved="true">
+  <proof prover="0"><undone/></proof>
+  <proof prover="1"><result status="valid" time="0.00"/></proof>
+  <proof prover="2"><result status="valid" time="0.00" steps="8"/></proof>
+  <proof prover="3"><result status="valid" time="0.00"/></proof>
+  <proof prover="4"><result status="valid" time="0.01"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP7/.Naturelle.aux b/TP7/.Naturelle.aux
new file mode 100755
index 0000000..9986a4a
--- /dev/null
+++ b/TP7/.Naturelle.aux
@@ -0,0 +1,40 @@
+COQAUX1 f13e540aa0997388dd1408b0662438d6 /home/lfainsin/1A/Modé/TP7/Naturelle.v
+383 387 proof_build_time "0.000"
+0 0 E_imp_th "0.000"
+383 387 context_used ""
+383 387 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+916 920 proof_build_time "0.000"
+0 0 E_forall_th "0.000"
+916 920 context_used ""
+916 920 proof_check_time "0.000"
+1291 1295 proof_build_time "0.001"
+0 0 E_et_g_th "0.001"
+1291 1295 context_used ""
+1291 1295 proof_check_time "0.000"
+1601 1605 proof_build_time "0.000"
+0 0 E_et_d_th "0.000"
+1601 1605 context_used ""
+1601 1605 proof_check_time "0.000"
+1983 1987 proof_build_time "0.001"
+0 0 E_ou_th "0.001"
+1983 1987 context_used ""
+1983 1987 proof_check_time "0.000"
+0 0 VernacProof "tac:no using:no"
+2806 2810 proof_build_time "0.001"
+0 0 E_exists_th "0.001"
+2806 2810 context_used ""
+2806 2810 proof_check_time "0.000"
+3280 3284 proof_build_time "0.000"
+0 0 E_antiT_th "0.000"
+3280 3284 context_used ""
+3280 3284 proof_check_time "0.000"
+3502 3506 proof_build_time "0.001"
+0 0 I_antiT_th "0.001"
+3502 3506 context_used ""
+3502 3506 proof_check_time "0.000"
+3683 3687 proof_build_time "0.000"
+0 0 I_non_th "0.000"
+3683 3687 context_used ""
+3683 3687 proof_check_time "0.000"
+0 0 vo_compile_time "0.107"
diff --git a/TP7/._Naturelle.v b/TP7/._Naturelle.v
new file mode 100755
index 0000000..9f9b07e
Binary files /dev/null and b/TP7/._Naturelle.v differ
diff --git a/TP7/Naturelle.glob b/TP7/Naturelle.glob
new file mode 100755
index 0000000..df9312d
--- /dev/null
+++ b/TP7/Naturelle.glob
@@ -0,0 +1,150 @@
+DIGEST f13e540aa0997388dd1408b0662438d6
+FNaturelle
+R15:23 Coq.Logic.Classical <> <> lib
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+prf 278:285 <> E_imp_th
+R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R337:339 Naturelle <> psi var
+R330:332 Naturelle <> phi var
+R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R322:324 Naturelle <> psi var
+R315:317 Naturelle <> phi var
+R443:450 Naturelle <> E_imp_th thm
+R521:528 Naturelle <> E_imp_th thm
+prf 816:826 <> E_forall_th
+R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R855:855 Naturelle <> A var
+R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R890:892 Naturelle <> phi var
+R894:894 Naturelle <> a var
+R880:882 Naturelle <> phi var
+R884:884 Naturelle <> x var
+R996:1006 Naturelle <> E_forall_th thm
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1105:1108 Coq.Init.Logic <> conj constr
+prf 1157:1165 <> E_et_g_th
+R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1210:1212 Naturelle <> phi var
+R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1195:1197 Naturelle <> phi var
+R1202:1204 Naturelle <> psi var
+R1352:1360 Naturelle <> E_et_g_th thm
+R1432:1440 Naturelle <> E_et_g_th thm
+prf 1465:1473 <> E_et_d_th
+R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1518:1520 Naturelle <> psi var
+R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
+R1503:1505 Naturelle <> phi var
+R1510:1512 Naturelle <> psi var
+R1662:1670 Naturelle <> E_et_d_th thm
+R1743:1751 Naturelle <> E_et_d_th thm
+prf 1776:1782 <> E_ou_th
+R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1863:1865 Naturelle <> chi var
+R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1855:1857 Naturelle <> chi var
+R1848:1850 Naturelle <> psi var
+R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R1839:1841 Naturelle <> chi var
+R1832:1834 Naturelle <> phi var
+R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R1816:1818 Naturelle <> phi var
+R1823:1825 Naturelle <> psi var
+R2042:2048 Naturelle <> E_ou_th thm
+R2124:2130 Naturelle <> E_ou_th thm
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2213:2221 Coq.Init.Logic <> or_introl constr
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R2324:2332 Coq.Init.Logic <> or_intror constr
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
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+R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2438:2438 Naturelle <> x var
+R2453:2460 Coq.Init.Logic <> ex_intro constr
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+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
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+R2583:2583 Naturelle <> x var
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+R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2583:2583 Naturelle <> x var
+R2597:2604 Coq.Init.Logic <> ex_intro constr
+prf 2669:2679 <> E_exists_th
+R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2708:2708 Naturelle <> A var
+R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2782:2784 Naturelle <> chi var
+R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R2774:2776 Naturelle <> chi var
+R2765:2767 Naturelle <> phi var
+R2769:2769 Naturelle <> a var
+R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
+R2744:2746 Naturelle <> phi var
+R2748:2748 Naturelle <> x var
+R2963:2973 Naturelle <> E_exists_th thm
+R3083:3085 Coq.Init.Logic <> not def
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
+R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3127:3131 Coq.Init.Logic <> False ind
+R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
+prf 3209:3218 <> E_antiT_th
+R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3252:3254 Naturelle <> phi var
+R3243:3247 Coq.Init.Logic <> False ind
+R3340:3349 Naturelle <> E_antiT_th thm
+prf 3370:3379 <> I_antiT_th
+R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3421:3425 Coq.Init.Logic <> False ind
+R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3413:3415 Naturelle <> phi var
+R3404:3406 Naturelle <> phi var
+R3435:3437 Coq.Init.Logic <> not def
+R3551:3555 Coq.Init.Logic <> False ind
+R3551:3555 Coq.Init.Logic <> False ind
+R3567:3576 Naturelle <> I_antiT_th thm
+prf 3598:3605 <> I_non_th
+R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3649:3651 Naturelle <> phi var
+R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
+R3638:3642 Coq.Init.Logic <> False ind
+R3631:3633 Naturelle <> phi var
+R3669:3671 Coq.Init.Logic <> not def
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
+R3745:3752 Naturelle <> I_non_th thm
+R3801:3810 Naturelle <> I_antiT_th thm
+R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm
diff --git a/TP7/Naturelle.v b/TP7/Naturelle.v
new file mode 100755
index 0000000..0546e4d
--- /dev/null
+++ b/TP7/Naturelle.v
@@ -0,0 +1,225 @@
+Require Export Classical.
+
+Ltac Hyp Nom := exact Nom.
+
+Ltac I_imp' :=
+  match goal with
+  | |- ?A -> ?B => let hyp := fresh "H" in intro hyp
+  | _           => fail
+  end.
+
+Ltac I_imp Nom :=
+  match goal with
+  | |- ?A -> ?B => intro Nom
+  | _           => fail
+  end.
+
+Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
+intros Pphi Ppsi Hphi2psi.
+Hyp Hphi2psi.
+Qed.
+
+Ltac E_imp' :=
+  match goal with
+  | |- ?P => eapply (E_imp_th _ P)
+  end.
+
+Ltac E_imp phi :=
+  match goal with
+  | |- ?P => apply (E_imp_th phi P)
+  end.
+
+Ltac I_forall' :=
+  match goal with
+  | |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
+  | _                      => fail
+  end.
+
+Ltac I_forall Nom :=
+  match goal with
+  | |- forall (x : ?A), ?P => intro Nom
+  | _                      => fail
+  end.
+
+Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
+Proof.
+firstorder.
+Qed.
+
+Ltac E_forall x :=
+  pattern x;
+  match goal with
+  | |- (?P x) => apply (E_forall_th _ P x)
+  | _         => fail
+  end.
+
+Ltac I_et :=
+  match goal with
+  | |- (?A /\ ?B) => apply (@conj A B)
+  | _             => fail
+  end.
+
+Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
+intros Pphi Ppsi Hphi_et_psi.
+elim Hphi_et_psi.
+intros Hphi Hpsi.
+Hyp Hphi.
+Qed.
+
+Ltac E_et_g' :=
+  match goal with
+  | |- ?P => eapply (E_et_g_th P _)
+  end.
+
+Ltac E_et_g psi :=
+  match goal with
+  | |- ?P => apply (E_et_g_th P psi)
+  end.
+
+Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
+intros Pphi Ppsi H_phi_et_psi.
+elim H_phi_et_psi.
+intros Hphi Hpsi.
+Hyp Hpsi.
+Qed.
+
+Ltac E_et_d' :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th _ P)
+  end.
+
+Ltac E_et_d phi :=
+  match goal with
+  | |- ?P => eapply (E_et_d_th phi P)
+  end.
+
+Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
+intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
+elim Hphi_ou_psi.
+Hyp Hphi_imp_chi.
+Hyp Hpsi_imp_chi.
+Qed.
+
+Ltac E_ou' :=
+  match goal with
+  | |- ?P => eapply (E_ou_th _ _ P)
+  end.
+
+Ltac E_ou phi psi :=
+  match goal with
+  | |- ?P => apply (E_ou_th phi psi P)
+  end.
+
+Ltac I_ou_g :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_introl A B)
+  | _             => fail
+  end.
+
+Ltac I_ou_d :=
+  match goal with
+  | |- (?A \/ ?B) => apply (@or_intror A B)
+  | _             => fail
+  end.
+
+Ltac I_exists' :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
+  | _                           => fail
+  end.
+
+Ltac I_exists t :=
+  match goal with
+  | |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
+  | _                           => fail
+  end.
+
+Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
+Proof.
+firstorder.
+Qed.
+(*
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P)
+  end.
+*)
+Ltac E_exists phi :=
+  match goal with
+  | |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
+  end.
+
+Ltac TE :=
+  unfold not;
+  match goal with
+  | |- (?P \/ (?P -> False)) => exact (classic P)
+  | _                        => fail
+  end.
+
+Theorem E_antiT_th : forall (phi : Prop), False -> phi.
+intros Pphi F.
+elim F.
+Qed.
+
+Ltac E_antiT :=
+  match goal with
+  | |- ?P => apply (E_antiT_th P)
+  end.
+
+Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
+unfold not.
+intro Pphi.
+intros Hphi Hnphi.
+cut Pphi.
+Hyp Hnphi.
+Hyp Hphi.
+Qed.
+
+Ltac I_antiT phi :=
+ match goal with
+ | |- False => apply (I_antiT_th phi)
+ end.
+
+Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
+intros.
+unfold not.
+exact H.
+Qed.
+
+Ltac I_non Nom :=
+ match goal with
+ | |- ~ ?P => apply (I_non_th P); intro Nom
+ end.
+
+Ltac E_non phi :=
+ apply (I_antiT_th phi).
+
+Ltac absurde Nom :=
+ match goal with
+ | |- ?P => apply (NNPP P); intro Nom
+ end.
+
+(*
+Ltac I_antiT phi := apply (I_antiT_th phi).
+
+Ltac absurde Nom phi :=
+match goal with
+| |- phi =>
+cut (phi \/ ~phi);
+[
+intros L;
+elim L;
+[
+auto
+|
+clear L;
+intro Nom;
+apply (E_antiT_th)
+]
+|
+apply (classic phi)
+]
+| _ => fail
+end.
+*)
+
diff --git a/TP7/Unnamed_coqscript_1.crashcoqide b/TP7/Unnamed_coqscript_1.crashcoqide
new file mode 100755
index 0000000..e69de29
diff --git a/TP7/coq-exercice-1.v b/TP7/coq-exercice-1.v
new file mode 100755
index 0000000..55f33e1
--- /dev/null
+++ b/TP7/coq-exercice-1.v
@@ -0,0 +1,29 @@
+Require Import Naturelle.
+Section Session1_2019_Logique_Exercice_1.
+
+Variable A B C : Prop.
+
+Theorem Exercice_1_Naturelle :  (A -> B -> C) -> ((A /\ B) -> C).
+I_imp H.
+I_imp H0.
+E_imp B.
+E_imp A.
+exact H.
+E_et_g B.
+exact H0.
+E_et_d A.
+exact H0.
+Qed.
+
+Theorem Exercice_1_Coq :  (A -> B -> C) -> ((A /\ B) -> C).
+intros.
+destruct H0.
+cut B.
+cut A.
+exact H.
+exact H0.
+exact H1.
+Qed.
+
+End Session1_2019_Logique_Exercice_1.
+
diff --git a/TP7/coq-exercice-2.v b/TP7/coq-exercice-2.v
new file mode 100755
index 0000000..3b10b1b
--- /dev/null
+++ b/TP7/coq-exercice-2.v
@@ -0,0 +1,15 @@
+Require Import Naturelle.
+Section Session1_2019_Logique_Exercice_2.
+
+Variable A B : Prop.
+
+Theorem Exercice_2_Naturelle : (~A) \/ B -> (~A) \/ (A /\ B).
+
+Theorem Exercice_2_Coq : (~A) \/ B -> (~A) \/ (A /\ B).
+intros.
+
+
+Qed.
+
+End Session1_2019_Logique_Exercice_2.
+
diff --git a/TP7/coq-exercice-3.v b/TP7/coq-exercice-3.v
new file mode 100755
index 0000000..3c3108e
--- /dev/null
+++ b/TP7/coq-exercice-3.v
@@ -0,0 +1,113 @@
+Section Session1_2019_Induction_Exercice_3.
+
+(* Déclaration d’un domaine pour les éléments des listes *)
+Variable A : Set.
+
+(* Déclaration d'un type liste générique d'éléments de type E *)
+Inductive liste (E : Set) : Set :=
+Nil
+: liste E
+| Cons : E -> liste E -> liste E.
+
+(* Déclaration du nom de la fonction append *)
+Variable append_spec : forall E : Set, liste E -> liste E -> liste E.
+
+(* Spécification du comportement de append pour Nil en premier paramètre *)
+Axiom append_Nil : forall E : Set, forall (l : liste E), append_spec E (Nil E) l = l.
+
+(* Spécification du comportement de append pour Cons en premier paramètre *)
+Axiom append_Cons : forall E : Set, forall (t : E), forall (q l : liste E),
+   append_spec E ((Cons E) t q) l = (Cons E) t (append_spec E q l).
+
+(* Spécification du comportement de append pour Nil en second paramètre *)
+Axiom append_Nil_right : forall E : Set, forall (l : liste E), (append_spec E l (Nil E)) = l.
+
+(* append est associative à gauche et à droite *)
+Axiom append_associative : forall E : Set, forall (l1 l2 l3 : liste E),
+   (append_spec E l1 (append_spec E l2 l3)) = (append_spec E (append_spec E l1 l2) l3).
+
+(* Déclaration du nom de la fonction flatten *)
+Variable flatten_spec : forall E : Set, liste (liste E) -> liste E.
+
+(* Spécification du comportement de flatten pour Nil *)
+Axiom flatten_Nil : forall E : Set, flatten_spec E (Nil (liste E)) = (Nil E).
+
+(* Spécification du comportement de flatten pour Cons *)
+Axiom flatten_Cons : forall E : Set, forall (t : liste E), forall (q : liste (liste E)),
+  flatten_spec E (Cons (liste E) t q) = append_spec E t (flatten_spec E q).
+
+(* Déclaration du nom de la fonction split *)
+Variable split_spec : forall E : Set, liste E -> liste (liste E).
+
+(* Spécification du comportement de split pour Nil *)
+Axiom split_Nil : forall E : Set, split_spec E (Nil E) = (Nil (liste E)).
+
+(* Spécification du comportement de split pour Cons *)
+Axiom split_Cons : forall E : Set, forall (t : E), forall (q : liste E),
+  split_spec E (Cons E t q) = Cons (liste E) (Cons E t (Nil E)) (split_spec E q).
+
+(* Cohérence de flatten et de split : flatten(split(l)) = l*)
+Theorem flatten_split_consistency : forall E : Set, forall (l : liste E),
+   flatten_spec E (split_spec E l) = l.
+intros.
+induction l.
+(* cas de base *)
+rewrite split_Nil.
+rewrite flatten_Nil.
+reflexivity.
+(* cas général *)
+rewrite split_Cons.
+rewrite flatten_Cons.
+rewrite append_Cons.
+rewrite append_Nil.
+rewrite IHl.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction append *)
+Fixpoint append_impl (E : Set) (l1 l2 : liste E) {struct l1} : liste E :=
+match l1 with
+Nil _ => l2
+| (Cons _ t1 q1) => (Cons E t1 (append_impl E q1 l2))
+end.
+
+Theorem append_correctness : forall E : Set, forall (l1 l2 : liste E),
+(append_spec E l1 l2) = (append_impl E l1 l2).
+intro TE.
+induction l1.
+intro Hl2.
+rewrite append_Nil.
+simpl.
+reflexivity.
+intro Hl2.
+rewrite append_Cons.
+simpl.
+rewrite IHl1.
+reflexivity.
+Qed.
+
+(* Implantation de la fonction flatten *)
+Fixpoint flatten_impl (E : Set) (l : liste (liste E)) {struct l} : liste E :=
+  match l with
+    Nil _ => Nil _
+    | (Cons _ t q) => (append_impl E t (flatten_impl E q ))
+end.
+
+(* Correction de l'implantation de flatten par rapport à sa spécification *)
+Theorem flatten_correctness : forall E : Set, forall (l : liste (liste E)),
+   (flatten_spec E l) = (flatten_impl E l).
+intros.
+induction l.
+(* cas de base *)
+rewrite flatten_Nil.
+simpl flatten_impl.
+reflexivity.
+(* cas général *)
+rewrite flatten_Cons.
+simpl flatten_impl.
+rewrite append_correctness.
+rewrite IHl.
+reflexivity.
+Qed.
+
+End Session1_2019_Induction_Exercice_3.
diff --git a/TP7/why3-exercice-4.mlw b/TP7/why3-exercice-4.mlw
new file mode 100755
index 0000000..ea8fff6
--- /dev/null
+++ b/TP7/why3-exercice-4.mlw
@@ -0,0 +1,24 @@
+(* BE : Session 1 2019 *)
+(* Implémentation de la fonction somme des premiers entiers par un algorithme ascendant *)
+
+module Somme
+
+  use int.Int
+  use int.ComputerDivision
+  use ref.Refint
+
+  let somme (n: int) : int
+    requires { n >= 0 }
+    ensures  { 2 * result = n * (n+1) }
+  =
+    let i = ref 0 in
+    let r = ref 0 in
+    while  (!i < n) do
+      invariant { !r * 2 = !i * ( !i + 1 ) && n >= !i}
+      variant   { n - !i }
+      i := (!i) + 1;
+      r :=  (!r) + (!i)
+    done;
+    !r
+
+end
diff --git a/TP7/why3-exercice-4/why3session.xml b/TP7/why3-exercice-4/why3session.xml
new file mode 100755
index 0000000..e2a07be
--- /dev/null
+++ b/TP7/why3-exercice-4/why3session.xml
@@ -0,0 +1,36 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
+"http://why3.lri.fr/why3session.dtd">
+<why3session shape_version="5">
+<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
+<file proved="true">
+<path name=".."/>
+<path name="why3-exercice-4.mlw"/>
+<theory name="Somme" proved="true">
+ <goal name="VC somme" expl="VC for somme" proved="true">
+ <transf name="split_vc" proved="true" >
+  <goal name="VC somme.0" expl="loop invariant init" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
+  </goal>
+  <goal name="VC somme.1" expl="loop variant decrease" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
+  </goal>
+  <goal name="VC somme.2" expl="loop invariant preservation" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
+  </goal>
+  <goal name="VC somme.3" expl="postcondition" proved="true">
+  <proof prover="0"><result status="valid" time="0.00" steps="5"/></proof>
+  <proof prover="1"><result status="valid" time="0.01"/></proof>
+  <proof prover="2"><result status="valid" time="0.01"/></proof>
+  <proof prover="3"><result status="valid" time="0.01"/></proof>
+  <proof prover="4"><result status="valid" time="0.01"/></proof>
+  </goal>
+ </transf>
+ </goal>
+</theory>
+</file>
+</why3session>
diff --git a/TP8-9/outils-unix/cmd-sed.txt b/TP8-9/outils-unix/cmd-sed.txt
new file mode 100755
index 0000000..0a48d78
--- /dev/null
+++ b/TP8-9/outils-unix/cmd-sed.txt
@@ -0,0 +1,2 @@
+sed -E -e "s/<\/?[a-z]+>//g" < enseignant-element.xml-sed
+sed -E -e "s/<\/?[a-z]+>//g" < enseignant-attribut.xml-sed
\ No newline at end of file
diff --git a/TP8-9/outils-unix/commandes-TP5.sh b/TP8-9/outils-unix/commandes-TP5.sh
new file mode 100755
index 0000000..7a5cc32
--- /dev/null
+++ b/TP8-9/outils-unix/commandes-TP5.sh
@@ -0,0 +1,11 @@
+#!/bin/sh
+echo "Affichage des lignes contenant des nombres entiers naturels :"
+egrep -e "\ ([0-9]+)$" exemple.txt 
+echo "Affichage des lignes contenant des nombres entiers relatifs :"
+egrep -e "\ ([+-]+[0-9]+)$" exemple.txt
+echo "Affichage des lignes contenant des nombres décimaux :"
+egrep -e "\ ([+-]?[0-9]+[.][0-9]+([eE][-+]?[1-9][0-9]*)?)$" exemple.txt
+echo "Affichage des lignes contenant des nombres rationnels :"
+egrep -e "\ ([+-]?[0-9]+/[1-9][0-9]*)$" exemple.txt
+echo "Affichage des lignes contenant des nombres complexes rationnels :"
+egrep -e "\ (([+-]?[0-9]+/[1-9][0-9]*)?[+-]?[0-9]+/[1-9][0-9]*i?)$" exemple.txt
diff --git a/TP8-9/outils-unix/enseignant-attribut.xml-sed.out b/TP8-9/outils-unix/enseignant-attribut.xml-sed.out
new file mode 100755
index 0000000..8970742
--- /dev/null
+++ b/TP8-9/outils-unix/enseignant-attribut.xml-sed.out
@@ -0,0 +1,5 @@
+
+     <identite prenom="Marc" nom="Pantel"/>
+     <discipline nom="Traduction des langages"/>
+     <discipline nom="Sémantique formelle"/>
+
diff --git a/TP8-9/outils-unix/enseignant-attribut.xml-vim b/TP8-9/outils-unix/enseignant-attribut.xml-vim
new file mode 100755
index 0000000..8970742
--- /dev/null
+++ b/TP8-9/outils-unix/enseignant-attribut.xml-vim
@@ -0,0 +1,5 @@
+
+     <identite prenom="Marc" nom="Pantel"/>
+     <discipline nom="Traduction des langages"/>
+     <discipline nom="Sémantique formelle"/>
+
diff --git a/TP8-9/outils-unix/enseignant-element.xml-sed.out b/TP8-9/outils-unix/enseignant-element.xml-sed.out
new file mode 100755
index 0000000..034c83d
--- /dev/null
+++ b/TP8-9/outils-unix/enseignant-element.xml-sed.out
@@ -0,0 +1,8 @@
+
+     
+          Marc
+          Pantel
+     
+     Traduction des langages
+     Sémantique formelle
+
diff --git a/TP8-9/outils-unix/enseignant-element.xml-vim b/TP8-9/outils-unix/enseignant-element.xml-vim
new file mode 100755
index 0000000..1a04f6d
--- /dev/null
+++ b/TP8-9/outils-unix/enseignant-element.xml-vim
@@ -0,0 +1,8 @@
+
+
+          Marc
+          Pantel
+
+     Traduction des langages
+     Sémantique formelle
+
diff --git a/TP8-9/outils-unix/exemple.txt b/TP8-9/outils-unix/exemple.txt
new file mode 100755
index 0000000..21b2513
--- /dev/null
+++ b/TP8-9/outils-unix/exemple.txt
@@ -0,0 +1,23 @@
+Suite de chiffres : 0123456789
+Entier naturel : 0
+Entier naturel : 123
+Entier relatif : +123
+Entier relatif : -123
+Décimal : 0.123
+Décimal : -0.123
+Décimal : 0.123e10
+Décimal : 0.123E10
+Décimal : -0.123e10
+Décimal : -0.123E10
+Décimal : 0.123e-10
+Décimal : 0.123E-10
+Décimal : -0.123e-10
+Décimal : -0.123e-10
+Rationnel : 1/2
+Rationnel : -1/2
+Complexe : 1/2i
+Complexe : -1/2i
+Complexe : 2/3+1/2i
+Complexe : 2/3+1/2i
+Complexe : -2/3-1/2i
+Complexe : -2/3-1/2i
diff --git a/TP8-9/process-analysis/MainProcessus b/TP8-9/process-analysis/MainProcessus
new file mode 100755
index 0000000..392f611
Binary files /dev/null and b/TP8-9/process-analysis/MainProcessus differ
diff --git a/TP8-9/process-analysis/Makefile b/TP8-9/process-analysis/Makefile
new file mode 100755
index 0000000..f436d80
--- /dev/null
+++ b/TP8-9/process-analysis/Makefile
@@ -0,0 +1,36 @@
+
+OCAMLLEX = ocamllex
+OCAMLYACC = menhir
+OCAMLC = ocamlc
+OCAMLLD = ocamlc
+
+
+.SUFFIXES: .ml .mli .cmo .cmi .mll .mly
+
+%.cmi : %.mli
+	$(OCAMLC) -c $<
+
+%.cmo : %.ml %.cmi
+	$(OCAMLC) -c $<
+
+%.cmo : %.ml
+	$(OCAMLC) -c $<
+
+%.cmo : %.cmi
+	$(OCAMLC) -c $<
+
+%.ml : %.mll
+	$(OCAMLLEX) $<
+
+%.mli %.ml : %.mly
+	$(OCAMLYACC) $<
+
+all : mainProcessus
+
+lexerProcessus.ml : parserProcessus.cmi
+
+mainProcessus : lexerProcessus.cmo parserProcessus.cmo mainProcessus.cmo
+	$(OCAMLC) -o MainProcessus lexerProcessus.cmo parserProcessus.cmo mainProcessus.cmo
+
+clean :
+	-rm -f *.cmo *.cmi lexerProcessus.ml parserProcessus.ml MainProcessus
diff --git a/TP8-9/process-analysis/lexerProcessus.ml b/TP8-9/process-analysis/lexerProcessus.ml
new file mode 100755
index 0000000..01a031c
--- /dev/null
+++ b/TP8-9/process-analysis/lexerProcessus.ml
@@ -0,0 +1,1279 @@
+# 1 "lexerProcessus.mll"
+ 
+
+(* Partie recopiée dans le fichier CaML généré. *)
+(* Ouverture de modules exploités dans les actions *)
+(* Déclarations de types, de constantes, de fonctions, d'exceptions exploités dans les actions *)
+
+  open ParserProcessus
+  exception LexicalError
+
+
+# 13 "lexerProcessus.ml"
+let __ocaml_lex_tables = {
+  Lexing.lex_base =
+   "\000\000\238\255\239\255\078\000\153\000\242\255\243\255\163\000\
+    \238\000\057\001\132\001\207\001\026\002\016\000\002\000\003\000\
+    \149\001\181\001\223\001\224\001\000\002\042\002\254\255\043\002\
+    \075\002\108\002\160\002\235\002\061\003\136\003\211\003\030\004\
+    \105\004\180\004\255\004\074\005\149\005\224\005\043\006\118\006\
+    \193\006\012\007\087\007\162\007\237\007\056\008\131\008\206\008\
+    \025\009\100\009\175\009\250\009\069\010\144\010\219\010\038\011\
+    \113\011\188\011\007\012\082\012\157\012\232\012\051\013\126\013\
+    \201\013\020\014\095\014\170\014\245\014\064\015\139\015\214\015\
+    \033\016";
+  Lexing.lex_backtrk =
+   "\255\255\255\255\255\255\015\000\014\000\255\255\255\255\015\000\
+    \015\000\015\000\015\000\015\000\015\000\017\000\000\000\001\000\
+    \255\255\255\255\001\000\255\255\255\255\001\000\255\255\255\255\
+    \255\255\001\000\015\000\015\000\015\000\015\000\015\000\002\000\
+    \015\000\015\000\015\000\015\000\015\000\015\000\015\000\003\000\
+    \015\000\015\000\015\000\010\000\015\000\015\000\015\000\015\000\
+    \015\000\004\000\007\000\015\000\015\000\015\000\015\000\015\000\
+    \015\000\008\000\005\000\006\000\015\000\015\000\015\000\015\000\
+    \015\000\015\000\015\000\009\000\015\000\015\000\015\000\015\000\
+    \011\000";
+  Lexing.lex_default =
+   "\001\000\000\000\000\000\255\255\255\255\000\000\000\000\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\015\000\
+    \019\000\023\000\019\000\019\000\023\000\019\000\000\000\023\000\
+    \023\000\023\000\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255";
+  Lexing.lex_trans =
+   "\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\014\000\014\000\014\000\014\000\255\255\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \014\000\000\000\014\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\013\000\
+    \004\000\004\000\004\000\004\000\004\000\004\000\004\000\004\000\
+    \004\000\004\000\016\000\000\000\000\000\000\000\000\000\015\000\
+    \000\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\000\000\000\000\000\000\000\000\003\000\
+    \000\000\011\000\003\000\003\000\003\000\003\000\009\000\003\000\
+    \003\000\008\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \012\000\003\000\007\000\010\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\006\000\000\000\005\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\000\000\000\000\000\000\000\000\003\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\004\000\004\000\004\000\004\000\004\000\004\000\004\000\
+    \004\000\004\000\004\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\000\000\000\000\
+    \002\000\000\000\003\000\255\255\003\000\003\000\003\000\003\000\
+    \060\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\000\000\000\000\000\000\000\000\003\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\059\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\000\000\000\000\000\000\000\000\
+    \003\000\000\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\051\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\000\000\017\000\
+    \000\000\000\000\000\000\000\000\018\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\017\000\
+    \000\000\000\000\000\000\003\000\022\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \044\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\017\000\020\000\000\000\000\000\000\000\018\000\021\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\020\000\000\000\000\000\000\000\003\000\022\000\
+    \003\000\003\000\033\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\032\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\020\000\024\000\000\000\000\000\
+    \000\000\021\000\025\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\024\000\000\000\000\000\
+    \000\000\003\000\022\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\026\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\255\255\024\000\000\000\
+    \000\000\000\000\000\000\025\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\255\255\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\000\000\000\000\000\000\000\000\000\000\255\255\
+    \255\255\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\000\000\000\000\000\000\000\000\003\000\
+    \255\255\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\027\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\000\000\000\000\000\000\
+    \000\000\000\000\255\255\255\255\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\000\000\000\000\
+    \000\000\000\000\003\000\255\255\003\000\003\000\028\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\255\255\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\000\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \000\000\000\000\000\000\000\000\003\000\000\000\003\000\003\000\
+    \003\000\003\000\029\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\000\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\000\000\000\000\000\000\000\000\003\000\
+    \000\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\030\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\000\000\000\000\000\000\
+    \000\000\000\000\000\000\000\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\000\000\000\000\
+    \000\000\000\000\003\000\000\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\031\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \000\000\000\000\000\000\000\000\000\000\000\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\000\000\000\000\000\000\000\000\003\000\000\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\000\000\000\000\000\000\000\000\000\000\
+    \000\000\000\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
+    \003\000\003\000\003\000\003\000\003\000\003\000\003\000\003\000\
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+    \255\255\067\000\255\255\067\000\067\000\067\000\067\000\067\000\
+    \067\000\067\000\067\000\067\000\067\000\067\000\067\000\067\000\
+    \067\000\067\000\067\000\067\000\067\000\067\000\067\000\067\000\
+    \067\000\067\000\067\000\067\000\067\000\068\000\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \255\255\255\255\255\255\255\255\068\000\255\255\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \068\000\068\000\068\000\068\000\068\000\068\000\068\000\068\000\
+    \069\000\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\255\255\255\255\255\255\255\255\069\000\
+    \255\255\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\069\000\069\000\069\000\069\000\069\000\
+    \069\000\069\000\069\000\070\000\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\255\255\255\255\
+    \255\255\255\255\070\000\255\255\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\070\000\070\000\
+    \070\000\070\000\070\000\070\000\070\000\070\000\071\000\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\255\255\255\255\255\255\255\255\071\000\255\255\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\071\000\071\000\071\000\071\000\071\000\071\000\071\000\
+    \071\000\072\000\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\255\255\255\255\255\255\255\255\
+    \072\000\255\255\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\072\000\072\000\072\000\072\000\
+    \072\000\072\000\072\000\072\000\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\255\
+    \255\255\255\255";
+  Lexing.lex_base_code =
+   "";
+  Lexing.lex_backtrk_code =
+   "";
+  Lexing.lex_default_code =
+   "";
+  Lexing.lex_trans_code =
+   "";
+  Lexing.lex_check_code =
+   "";
+  Lexing.lex_code =
+   "";
+}
+
+let rec main lexbuf =
+   __ocaml_lex_main_rec lexbuf 0
+and __ocaml_lex_main_rec lexbuf __ocaml_lex_state =
+  match Lexing.engine __ocaml_lex_tables __ocaml_lex_state lexbuf with
+      | 0 ->
+# 25 "lexerProcessus.mll"
+                        ( main lexbuf )
+# 1169 "lexerProcessus.ml"
+
+  | 1 ->
+# 26 "lexerProcessus.mll"
+                    ( (main lexbuf) )
+# 1174 "lexerProcessus.ml"
+
+  | 2 ->
+# 27 "lexerProcessus.mll"
+                  ( PROCESS )
+# 1179 "lexerProcessus.ml"
+
+  | 3 ->
+# 28 "lexerProcessus.mll"
+                   ( ACTIVITY )
+# 1184 "lexerProcessus.ml"
+
+  | 4 ->
+# 29 "lexerProcessus.mll"
+                 ( STARTS )
+# 1189 "lexerProcessus.ml"
+
+  | 5 ->
+# 30 "lexerProcessus.mll"
+                   ( FINISHES )
+# 1194 "lexerProcessus.ml"
+
+  | 6 ->
+# 31 "lexerProcessus.mll"
+             ( IF )
+# 1199 "lexerProcessus.ml"
+
+  | 7 ->
+# 32 "lexerProcessus.mll"
+                  ( STARTED )
+# 1204 "lexerProcessus.ml"
+
+  | 8 ->
+# 33 "lexerProcessus.mll"
+                          ( FINISHED )
+# 1209 "lexerProcessus.ml"
+
+  | 9 ->
+# 34 "lexerProcessus.mll"
+                   ( RESOURCE )
+# 1214 "lexerProcessus.ml"
+
+  | 10 ->
+# 35 "lexerProcessus.mll"
+                 ( AMOUNT )
+# 1219 "lexerProcessus.ml"
+
+  | 11 ->
+# 36 "lexerProcessus.mll"
+                      ( REQUIRES )
+# 1224 "lexerProcessus.ml"
+
+  | 12 ->
+# 37 "lexerProcessus.mll"
+             ( LEFT_BRACE )
+# 1229 "lexerProcessus.ml"
+
+  | 13 ->
+# 38 "lexerProcessus.mll"
+             ( RIGHT_BRACE )
+# 1234 "lexerProcessus.ml"
+
+  | 14 ->
+let
+# 39 "lexerProcessus.mll"
+                texte
+# 1240 "lexerProcessus.ml"
+= Lexing.sub_lexeme lexbuf lexbuf.Lexing.lex_start_pos lexbuf.Lexing.lex_curr_pos in
+# 39 "lexerProcessus.mll"
+                         ( (NUMBER (int_of_string texte)) )
+# 1244 "lexerProcessus.ml"
+
+  | 15 ->
+let
+# 40 "lexerProcessus.mll"
+                                      texte
+# 1250 "lexerProcessus.ml"
+= Lexing.sub_lexeme lexbuf lexbuf.Lexing.lex_start_pos lexbuf.Lexing.lex_curr_pos in
+# 40 "lexerProcessus.mll"
+                                            ( (IDENTIFIER texte) )
+# 1254 "lexerProcessus.ml"
+
+  | 16 ->
+# 41 "lexerProcessus.mll"
+             ( END )
+# 1259 "lexerProcessus.ml"
+
+  | 17 ->
+let
+# 42 "lexerProcessus.mll"
+         texte
+# 1265 "lexerProcessus.ml"
+= Lexing.sub_lexeme_char lexbuf lexbuf.Lexing.lex_start_pos in
+# 42 "lexerProcessus.mll"
+                    ( (print_string "Erreur lexicale : ");(print_char texte);(print_newline ()); (main lexbuf) )
+# 1269 "lexerProcessus.ml"
+
+  | __ocaml_lex_state -> lexbuf.Lexing.refill_buff lexbuf;
+      __ocaml_lex_main_rec lexbuf __ocaml_lex_state
+
+;;
+
+# 44 "lexerProcessus.mll"
+ 
+
+
+# 1280 "lexerProcessus.ml"
diff --git a/TP8-9/process-analysis/lexerProcessus.mll b/TP8-9/process-analysis/lexerProcessus.mll
new file mode 100755
index 0000000..e241443
--- /dev/null
+++ b/TP8-9/process-analysis/lexerProcessus.mll
@@ -0,0 +1,46 @@
+{
+
+(* Partie recopiée dans le fichier CaML généré. *)
+(* Ouverture de modules exploités dans les actions *)
+(* Déclarations de types, de constantes, de fonctions, d'exceptions exploités dans les actions *)
+
+  open ParserProcessus
+  exception LexicalError
+
+}
+
+(* Déclaration d'expressions régulières exploitées par la suite *)
+let chiffre = ['0' - '9']
+let minuscule = ['a' - 'z']
+let majuscule = ['A' - 'Z']
+let lettre = minuscule | majuscule
+let lettre_chiffre = lettre | chiffre | '_'
+let commentaire =
+  (* Commentaire bloc à la C/C++/C#/Java/etc *)
+  ("/*" [^ '*']* '*'* ([^ '*' '/'] [^ '*']* '*'*)* '/')
+  (* Commentaire fin de ligne à la C/C++/C#/Java/etc  *)
+  |  "//" [^'\n']*
+
+rule main = parse
+  | ['\n' '\t' ' ']+				{ main lexbuf }
+  | commentaire					{ (main lexbuf) }
+  | "process"					{ PROCESS }
+  | "activity"					{ ACTIVITY }
+  | "starts"					{ STARTS }
+  | "finishes"					{ FINISHES }
+  | "if"					{ IF }
+  | "started"					{ STARTED }
+  | "finished"				       	{ FINISHED }
+  | "resource"					{ RESOURCE }
+  | "amount"					{ AMOUNT }
+  | "requires"        { REQUIRES }
+  | "{"						{ LEFT_BRACE }
+  | "}"						{ RIGHT_BRACE }
+  | chiffre+ as texte				{ (NUMBER (int_of_string texte)) }
+  | ('_' | lettre) lettre_chiffre* as texte	{ (IDENTIFIER texte) }
+  | eof						{ END }
+  | _ as texte				 	{ (print_string "Erreur lexicale : ");(print_char texte);(print_newline ()); (main lexbuf) }
+
+{
+
+}
diff --git a/TP8-9/process-analysis/mainProcessus.ml b/TP8-9/process-analysis/mainProcessus.ml
new file mode 100755
index 0000000..6d9b005
--- /dev/null
+++ b/TP8-9/process-analysis/mainProcessus.ml
@@ -0,0 +1,42 @@
+open ParserProcessus
+
+(* Fonction d'affichage des unités lexicales et des données qu'elles contiennent *)
+let printToken t =
+  (print_endline
+     ("token: " ^ (match t with
+       | PROCESS -> "process"
+       | IDENTIFIER (texte) -> ("identifier(" ^ texte ^ ")")
+       | ACTIVITY -> "activity"
+       | STARTS -> "starts"
+       | FINISHES -> "finishes"
+       | IF -> "if"
+       | STARTED -> "started"
+       | FINISHED -> "finished"
+       | RESOURCE -> "resource"
+       | REQUIRES -> "requires"
+       | AMOUNT -> "amount"
+       | LEFT_BRACE -> "{"
+       | RIGHT_BRACE -> "}"
+       | NUMBER (texte) -> ("number(" ^ (string_of_int texte) ^ ")")
+       | END -> "EOF"
+       )));;
+
+(* Analyse lexicale du fichier passé en paramètre de la ligne de commande *)
+if (Array.length Sys.argv > 1)
+then
+  let lexbuf = (Lexing.from_channel (open_in Sys.argv.(1))) in
+  let token = ref (LexerProcessus.main lexbuf) in
+  while ((!token) != END) do
+    (printToken (!token));
+    (token := (LexerProcessus.main lexbuf))
+  done
+else
+  (print_endline "MainMuProcessus fichier");;
+
+(* Analyse lexicale, syntaxique et sémantique du fichier passé en paramètre de la ligne de commande *)
+if (Array.length Sys.argv > 1)
+then
+  let lexbuf = (Lexing.from_channel (open_in Sys.argv.(1))) in
+  (ParserProcessus.fichier LexerProcessus.main lexbuf)
+else
+  (print_endline "MainProcessus fichier");;
diff --git a/TP8-9/process-analysis/parserProcessus.ml b/TP8-9/process-analysis/parserProcessus.ml
new file mode 100755
index 0000000..b7cb145
--- /dev/null
+++ b/TP8-9/process-analysis/parserProcessus.ml
@@ -0,0 +1,945 @@
+
+module MenhirBasics = struct
+  
+  exception Error
+  
+  type token = 
+    | STARTS
+    | STARTED
+    | RIGHT_BRACE
+    | RESOURCE
+    | REQUIRES
+    | PROCESS
+    | NUMBER of (
+# 15 "parserProcessus.mly"
+       (int)
+# 17 "parserProcessus.ml"
+  )
+    | LEFT_BRACE
+    | IF
+    | IDENTIFIER of (
+# 16 "parserProcessus.mly"
+       (string)
+# 24 "parserProcessus.ml"
+  )
+    | FINISHES
+    | FINISHED
+    | END
+    | AMOUNT
+    | ACTIVITY
+  
+end
+
+include MenhirBasics
+
+let _eRR =
+  MenhirBasics.Error
+
+type _menhir_env = {
+  _menhir_lexer: Lexing.lexbuf -> token;
+  _menhir_lexbuf: Lexing.lexbuf;
+  _menhir_token: token;
+  mutable _menhir_error: bool
+}
+
+and _menhir_state = 
+  | MenhirState30
+  | MenhirState21
+  | MenhirState19
+  | MenhirState17
+  | MenhirState14
+  | MenhirState9
+  | MenhirState3
+
+# 1 "parserProcessus.mly"
+  
+
+(* Partie recopiee dans le fichier CaML genere. *)
+(* Ouverture de modules exploites dans les actions *)
+(* Declarations de types, de constantes, de fonctions, d'exceptions exploites dans les actions *)
+
+
+# 63 "parserProcessus.ml"
+
+let rec _menhir_goto_etat : _menhir_env -> 'ttv_tail -> 'tv_etat -> 'ttv_return =
+  fun _menhir_env _menhir_stack _v ->
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : (('freshtv155 * _menhir_state * 'tv_action)) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 71 "parserProcessus.ml"
+    )) = Obj.magic _menhir_stack in
+    let (_v : 'tv_etat) = _v in
+    ((let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : (('freshtv153 * _menhir_state * 'tv_action)) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 78 "parserProcessus.ml"
+    )) = Obj.magic _menhir_stack in
+    let ((_4 : 'tv_etat) : 'tv_etat) = _v in
+    ((let ((_menhir_stack, _menhir_s, (_1 : 'tv_action)), (_3 : (
+# 16 "parserProcessus.mly"
+       (string)
+# 84 "parserProcessus.ml"
+    ))) = _menhir_stack in
+    let _2 = () in
+    let _v : 'tv_contrainte = 
+# 49 "parserProcessus.mly"
+                                       ( (print_endline "contrainte : action if IDENTIFIER etat") )
+# 90 "parserProcessus.ml"
+     in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv151) = _menhir_stack in
+    let (_menhir_s : _menhir_state) = _menhir_s in
+    let (_v : 'tv_contrainte) = _v in
+    ((let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv149 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
+    ((assert (not _menhir_env._menhir_error);
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | FINISHES ->
+        _menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState21
+    | LEFT_BRACE ->
+        _menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState21
+    | REQUIRES ->
+        _menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState21
+    | STARTS ->
+        _menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState21
+    | ACTIVITY | RESOURCE | RIGHT_BRACE ->
+        _menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState21
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState21) : 'freshtv150)) : 'freshtv152)) : 'freshtv154)) : 'freshtv156)
+
+and _menhir_fail : unit -> 'a =
+  fun () ->
+    Printf.fprintf stderr "Internal failure -- please contact the parser generator's developers.\n%!";
+    assert false
+
+and _menhir_goto_contraintes : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_contraintes -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s _v ->
+    match _menhir_s with
+    | MenhirState19 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv129 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_contraintes) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv127 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
+        let (_ : _menhir_state) = _menhir_s in
+        let ((_2 : 'tv_contraintes) : 'tv_contraintes) = _v in
+        ((let (_menhir_stack, _menhir_s, (_1 : 'tv_requires)) = _menhir_stack in
+        let _v : 'tv_contraintes = 
+# 43 "parserProcessus.mly"
+                                      ( (print_endline "contraintes : requires contraintes") )
+# 138 "parserProcessus.ml"
+         in
+        _menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv128)) : 'freshtv130)
+    | MenhirState21 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv133 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_contraintes) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv131 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
+        let (_ : _menhir_state) = _menhir_s in
+        let ((_2 : 'tv_contraintes) : 'tv_contraintes) = _v in
+        ((let (_menhir_stack, _menhir_s, (_1 : 'tv_contrainte)) = _menhir_stack in
+        let _v : 'tv_contraintes = 
+# 44 "parserProcessus.mly"
+                                       ( (print_endline "contraintes : contrainte contraintes") )
+# 154 "parserProcessus.ml"
+         in
+        _menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv132)) : 'freshtv134)
+    | MenhirState17 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : (('freshtv137 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_contraintes) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : (('freshtv135 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
+        let (_ : _menhir_state) = _menhir_s in
+        let ((_4 : 'tv_contraintes) : 'tv_contraintes) = _v in
+        ((let ((_menhir_stack, _menhir_s), _, (_2 : 'tv_elements)) = _menhir_stack in
+        let _3 = () in
+        let _1 = () in
+        let _v : 'tv_contraintes = 
+# 45 "parserProcessus.mly"
+                                                            ( (print_endline "contraintes : { elements } contraintes") )
+# 172 "parserProcessus.ml"
+         in
+        _menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv136)) : 'freshtv138)
+    | MenhirState9 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv147 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 180 "parserProcessus.ml"
+        )) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_contraintes) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv145 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 188 "parserProcessus.ml"
+        )) = Obj.magic _menhir_stack in
+        let (_ : _menhir_state) = _menhir_s in
+        let ((_3 : 'tv_contraintes) : 'tv_contraintes) = _v in
+        ((let ((_menhir_stack, _menhir_s), (_2 : (
+# 16 "parserProcessus.mly"
+       (string)
+# 195 "parserProcessus.ml"
+        ))) = _menhir_stack in
+        let _1 = () in
+        let _v : 'tv_activite = 
+# 40 "parserProcessus.mly"
+                                           ( (print_endline "activite : activity IDENTIFIER contraintes") )
+# 201 "parserProcessus.ml"
+         in
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv143) = _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_activite) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv141) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let (_v : 'tv_activite) = _v in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv139) = Obj.magic _menhir_stack in
+        let (_menhir_s : _menhir_state) = _menhir_s in
+        let ((_1 : 'tv_activite) : 'tv_activite) = _v in
+        ((let _v : 'tv_element = 
+# 35 "parserProcessus.mly"
+                   ( (print_endline "element : activite") )
+# 218 "parserProcessus.ml"
+         in
+        _menhir_goto_element _menhir_env _menhir_stack _menhir_s _v) : 'freshtv140)) : 'freshtv142)) : 'freshtv144)) : 'freshtv146)) : 'freshtv148)
+    | _ ->
+        _menhir_fail ()
+
+and _menhir_goto_action : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_action -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s _v ->
+    let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv125 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
+    ((assert (not _menhir_env._menhir_error);
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | IF ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv121 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
+        ((let _menhir_env = _menhir_discard _menhir_env in
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | IDENTIFIER _v ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv117 * _menhir_state * 'tv_action)) = Obj.magic _menhir_stack in
+            let (_v : (
+# 16 "parserProcessus.mly"
+       (string)
+# 244 "parserProcessus.ml"
+            )) = _v in
+            ((let _menhir_stack = (_menhir_stack, _v) in
+            let _menhir_env = _menhir_discard _menhir_env in
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | FINISHED ->
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv109) = Obj.magic _menhir_stack in
+                ((let _menhir_env = _menhir_discard _menhir_env in
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv107) = Obj.magic _menhir_stack in
+                ((let _1 = () in
+                let _v : 'tv_etat = 
+# 55 "parserProcessus.mly"
+                    ( (print_endline "etat : FINISHED") )
+# 260 "parserProcessus.ml"
+                 in
+                _menhir_goto_etat _menhir_env _menhir_stack _v) : 'freshtv108)) : 'freshtv110)
+            | STARTED ->
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv113) = Obj.magic _menhir_stack in
+                ((let _menhir_env = _menhir_discard _menhir_env in
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv111) = Obj.magic _menhir_stack in
+                ((let _1 = () in
+                let _v : 'tv_etat = 
+# 54 "parserProcessus.mly"
+               ( (print_endline "etat : STARTED") )
+# 273 "parserProcessus.ml"
+                 in
+                _menhir_goto_etat _menhir_env _menhir_stack _v) : 'freshtv112)) : 'freshtv114)
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : (('freshtv115 * _menhir_state * 'tv_action)) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 283 "parserProcessus.ml"
+                )) = Obj.magic _menhir_stack in
+                ((let ((_menhir_stack, _menhir_s, _), _) = _menhir_stack in
+                _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv116)) : 'freshtv118)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv119 * _menhir_state * 'tv_action)) = Obj.magic _menhir_stack in
+            ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv120)) : 'freshtv122)
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv123 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv124)) : 'freshtv126)
+
+and _menhir_goto_elements : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_elements -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s _v ->
+    let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
+    match _menhir_s with
+    | MenhirState14 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv77 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+        ((assert (not _menhir_env._menhir_error);
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | RIGHT_BRACE ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv73 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+            ((let _menhir_env = _menhir_discard _menhir_env in
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | FINISHES ->
+                _menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState17
+            | LEFT_BRACE ->
+                _menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState17
+            | REQUIRES ->
+                _menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState17
+            | STARTS ->
+                _menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState17
+            | ACTIVITY | RESOURCE | RIGHT_BRACE ->
+                _menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState17
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState17) : 'freshtv74)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv75 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+            ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv76)) : 'freshtv78)
+    | MenhirState30 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv81 * _menhir_state * 'tv_element) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+        ((let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv79 * _menhir_state * 'tv_element) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+        ((let ((_menhir_stack, _menhir_s, (_1 : 'tv_element)), _, (_2 : 'tv_elements)) = _menhir_stack in
+        let _v : 'tv_elements = 
+# 33 "parserProcessus.mly"
+                                 ( (print_endline "elements : element elements") )
+# 348 "parserProcessus.ml"
+         in
+        _menhir_goto_elements _menhir_env _menhir_stack _menhir_s _v) : 'freshtv80)) : 'freshtv82)
+    | MenhirState3 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ((('freshtv105) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 356 "parserProcessus.ml"
+        ))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+        ((assert (not _menhir_env._menhir_error);
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | RIGHT_BRACE ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ((('freshtv101) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 366 "parserProcessus.ml"
+            ))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+            ((let _menhir_env = _menhir_discard _menhir_env in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ((('freshtv99) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 373 "parserProcessus.ml"
+            ))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+            ((let ((_menhir_stack, (_2 : (
+# 16 "parserProcessus.mly"
+       (string)
+# 378 "parserProcessus.ml"
+            ))), _, (_4 : 'tv_elements)) = _menhir_stack in
+            let _5 = () in
+            let _3 = () in
+            let _1 = () in
+            let _v : 'tv_processus = 
+# 30 "parserProcessus.mly"
+                                                               ( (print_endline "processus : process IDENTIFIER { elements }") )
+# 386 "parserProcessus.ml"
+             in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv97) = _menhir_stack in
+            let (_v : 'tv_processus) = _v in
+            ((let _menhir_stack = (_menhir_stack, _v) in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv95 * 'tv_processus) = Obj.magic _menhir_stack in
+            ((assert (not _menhir_env._menhir_error);
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | END ->
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv91 * 'tv_processus) = Obj.magic _menhir_stack in
+                ((let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv89 * 'tv_processus) = Obj.magic _menhir_stack in
+                ((let (_menhir_stack, (_1 : 'tv_processus)) = _menhir_stack in
+                let _2 = () in
+                let _v : (
+# 21 "parserProcessus.mly"
+      (unit)
+# 407 "parserProcessus.ml"
+                ) = 
+# 28 "parserProcessus.mly"
+                        ( (print_endline "fichier : processus END") )
+# 411 "parserProcessus.ml"
+                 in
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv87) = _menhir_stack in
+                let (_v : (
+# 21 "parserProcessus.mly"
+      (unit)
+# 418 "parserProcessus.ml"
+                )) = _v in
+                ((let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv85) = Obj.magic _menhir_stack in
+                let (_v : (
+# 21 "parserProcessus.mly"
+      (unit)
+# 425 "parserProcessus.ml"
+                )) = _v in
+                ((let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv83) = Obj.magic _menhir_stack in
+                let ((_1 : (
+# 21 "parserProcessus.mly"
+      (unit)
+# 432 "parserProcessus.ml"
+                )) : (
+# 21 "parserProcessus.mly"
+      (unit)
+# 436 "parserProcessus.ml"
+                )) = _v in
+                (Obj.magic _1 : 'freshtv84)) : 'freshtv86)) : 'freshtv88)) : 'freshtv90)) : 'freshtv92)
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv93 * 'tv_processus) = Obj.magic _menhir_stack in
+                (raise _eRR : 'freshtv94)) : 'freshtv96)) : 'freshtv98)) : 'freshtv100)) : 'freshtv102)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ((('freshtv103) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 452 "parserProcessus.ml"
+            ))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
+            ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv104)) : 'freshtv106)
+    | _ ->
+        _menhir_fail ()
+
+and _menhir_goto_element : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_element -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s _v ->
+    let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv71 * _menhir_state * 'tv_element) = Obj.magic _menhir_stack in
+    ((assert (not _menhir_env._menhir_error);
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | ACTIVITY ->
+        _menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState30
+    | RESOURCE ->
+        _menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState30
+    | RIGHT_BRACE ->
+        _menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState30
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState30) : 'freshtv72)
+
+and _menhir_reduce5 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _v : 'tv_contraintes = 
+# 42 "parserProcessus.mly"
+                                     ( (print_endline "contraintes : /* Lambda, mot vide */") )
+# 483 "parserProcessus.ml"
+     in
+    _menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v
+
+and _menhir_run10 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_env = _menhir_discard _menhir_env in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv69) = Obj.magic _menhir_stack in
+    let (_menhir_s : _menhir_state) = _menhir_s in
+    ((let _1 = () in
+    let _v : 'tv_action = 
+# 51 "parserProcessus.mly"
+                ( (print_endline "action : STARTS") )
+# 497 "parserProcessus.ml"
+     in
+    _menhir_goto_action _menhir_env _menhir_stack _menhir_s _v) : 'freshtv70)
+
+and _menhir_run11 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_stack = (_menhir_stack, _menhir_s) in
+    let _menhir_env = _menhir_discard _menhir_env in
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | NUMBER _v ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv65 * _menhir_state) = Obj.magic _menhir_stack in
+        let (_v : (
+# 15 "parserProcessus.mly"
+       (int)
+# 513 "parserProcessus.ml"
+        )) = _v in
+        ((let _menhir_stack = (_menhir_stack, _v) in
+        let _menhir_env = _menhir_discard _menhir_env in
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | IDENTIFIER _v ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv61 * _menhir_state) * (
+# 15 "parserProcessus.mly"
+       (int)
+# 524 "parserProcessus.ml"
+            )) = Obj.magic _menhir_stack in
+            let (_v : (
+# 16 "parserProcessus.mly"
+       (string)
+# 529 "parserProcessus.ml"
+            )) = _v in
+            ((let _menhir_env = _menhir_discard _menhir_env in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv59 * _menhir_state) * (
+# 15 "parserProcessus.mly"
+       (int)
+# 536 "parserProcessus.ml"
+            )) = Obj.magic _menhir_stack in
+            let ((_3 : (
+# 16 "parserProcessus.mly"
+       (string)
+# 541 "parserProcessus.ml"
+            )) : (
+# 16 "parserProcessus.mly"
+       (string)
+# 545 "parserProcessus.ml"
+            )) = _v in
+            ((let ((_menhir_stack, _menhir_s), (_2 : (
+# 15 "parserProcessus.mly"
+       (int)
+# 550 "parserProcessus.ml"
+            ))) = _menhir_stack in
+            let _1 = () in
+            let _v : 'tv_requires = 
+# 47 "parserProcessus.mly"
+                                      ( (print_endline "requires : requires NUMBER IDENTIFIER") )
+# 556 "parserProcessus.ml"
+             in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv57) = _menhir_stack in
+            let (_menhir_s : _menhir_state) = _menhir_s in
+            let (_v : 'tv_requires) = _v in
+            ((let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv55 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
+            ((assert (not _menhir_env._menhir_error);
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | FINISHES ->
+                _menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState19
+            | LEFT_BRACE ->
+                _menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState19
+            | REQUIRES ->
+                _menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState19
+            | STARTS ->
+                _menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState19
+            | ACTIVITY | RESOURCE | RIGHT_BRACE ->
+                _menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState19
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState19) : 'freshtv56)) : 'freshtv58)) : 'freshtv60)) : 'freshtv62)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv63 * _menhir_state) * (
+# 15 "parserProcessus.mly"
+       (int)
+# 589 "parserProcessus.ml"
+            )) = Obj.magic _menhir_stack in
+            ((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv64)) : 'freshtv66)
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv67 * _menhir_state) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv68)
+
+and _menhir_run14 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_stack = (_menhir_stack, _menhir_s) in
+    let _menhir_env = _menhir_discard _menhir_env in
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | ACTIVITY ->
+        _menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState14
+    | RESOURCE ->
+        _menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState14
+    | RIGHT_BRACE ->
+        _menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState14
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState14
+
+and _menhir_run18 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_env = _menhir_discard _menhir_env in
+    let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv53) = Obj.magic _menhir_stack in
+    let (_menhir_s : _menhir_state) = _menhir_s in
+    ((let _1 = () in
+    let _v : 'tv_action = 
+# 52 "parserProcessus.mly"
+                    ( (print_endline "action : FINISHES") )
+# 628 "parserProcessus.ml"
+     in
+    _menhir_goto_action _menhir_env _menhir_stack _menhir_s _v) : 'freshtv54)
+
+and _menhir_errorcase : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    match _menhir_s with
+    | MenhirState30 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv39 * _menhir_state * 'tv_element) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv40)
+    | MenhirState21 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv41 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv42)
+    | MenhirState19 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv43 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv44)
+    | MenhirState17 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : (('freshtv45 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv46)
+    | MenhirState14 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv47 * _menhir_state) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv48)
+    | MenhirState9 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : ('freshtv49 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 665 "parserProcessus.ml"
+        )) = Obj.magic _menhir_stack in
+        ((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv50)
+    | MenhirState3 ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : (('freshtv51) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 674 "parserProcessus.ml"
+        ))) = Obj.magic _menhir_stack in
+        (raise _eRR : 'freshtv52)
+
+and _menhir_reduce11 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _v : 'tv_elements = 
+# 32 "parserProcessus.mly"
+                                  ( (print_endline "elements : /* Lambda, mot vide */") )
+# 683 "parserProcessus.ml"
+     in
+    _menhir_goto_elements _menhir_env _menhir_stack _menhir_s _v
+
+and _menhir_run4 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_stack = (_menhir_stack, _menhir_s) in
+    let _menhir_env = _menhir_discard _menhir_env in
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | IDENTIFIER _v ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv35 * _menhir_state) = Obj.magic _menhir_stack in
+        let (_v : (
+# 16 "parserProcessus.mly"
+       (string)
+# 699 "parserProcessus.ml"
+        )) = _v in
+        ((let _menhir_stack = (_menhir_stack, _v) in
+        let _menhir_env = _menhir_discard _menhir_env in
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | AMOUNT ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv31 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 710 "parserProcessus.ml"
+            )) = Obj.magic _menhir_stack in
+            ((let _menhir_env = _menhir_discard _menhir_env in
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | NUMBER _v ->
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : (('freshtv27 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 720 "parserProcessus.ml"
+                ))) = Obj.magic _menhir_stack in
+                let (_v : (
+# 15 "parserProcessus.mly"
+       (int)
+# 725 "parserProcessus.ml"
+                )) = _v in
+                ((let _menhir_env = _menhir_discard _menhir_env in
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : (('freshtv25 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 732 "parserProcessus.ml"
+                ))) = Obj.magic _menhir_stack in
+                let ((_4 : (
+# 15 "parserProcessus.mly"
+       (int)
+# 737 "parserProcessus.ml"
+                )) : (
+# 15 "parserProcessus.mly"
+       (int)
+# 741 "parserProcessus.ml"
+                )) = _v in
+                ((let ((_menhir_stack, _menhir_s), (_2 : (
+# 16 "parserProcessus.mly"
+       (string)
+# 746 "parserProcessus.ml"
+                ))) = _menhir_stack in
+                let _3 = () in
+                let _1 = () in
+                let _v : 'tv_resource = 
+# 38 "parserProcessus.mly"
+                                             ( (print_endline "resource : resource IDENTIFIER amount NUMBER") )
+# 753 "parserProcessus.ml"
+                 in
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv23) = _menhir_stack in
+                let (_menhir_s : _menhir_state) = _menhir_s in
+                let (_v : 'tv_resource) = _v in
+                ((let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv21) = Obj.magic _menhir_stack in
+                let (_menhir_s : _menhir_state) = _menhir_s in
+                let (_v : 'tv_resource) = _v in
+                ((let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : 'freshtv19) = Obj.magic _menhir_stack in
+                let (_menhir_s : _menhir_state) = _menhir_s in
+                let ((_1 : 'tv_resource) : 'tv_resource) = _v in
+                ((let _v : 'tv_element = 
+# 36 "parserProcessus.mly"
+                ( (print_endline "element : resource") )
+# 770 "parserProcessus.ml"
+                 in
+                _menhir_goto_element _menhir_env _menhir_stack _menhir_s _v) : 'freshtv20)) : 'freshtv22)) : 'freshtv24)) : 'freshtv26)) : 'freshtv28)
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : (('freshtv29 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 780 "parserProcessus.ml"
+                ))) = Obj.magic _menhir_stack in
+                ((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
+                _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv30)) : 'freshtv32)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : ('freshtv33 * _menhir_state) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 791 "parserProcessus.ml"
+            )) = Obj.magic _menhir_stack in
+            ((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv34)) : 'freshtv36)
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv37 * _menhir_state) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv38)
+
+and _menhir_run8 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
+  fun _menhir_env _menhir_stack _menhir_s ->
+    let _menhir_stack = (_menhir_stack, _menhir_s) in
+    let _menhir_env = _menhir_discard _menhir_env in
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | IDENTIFIER _v ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv15 * _menhir_state) = Obj.magic _menhir_stack in
+        let (_v : (
+# 16 "parserProcessus.mly"
+       (string)
+# 815 "parserProcessus.ml"
+        )) = _v in
+        ((let _menhir_stack = (_menhir_stack, _v) in
+        let _menhir_env = _menhir_discard _menhir_env in
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | FINISHES ->
+            _menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState9
+        | LEFT_BRACE ->
+            _menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState9
+        | REQUIRES ->
+            _menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState9
+        | STARTS ->
+            _menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState9
+        | ACTIVITY | RESOURCE | RIGHT_BRACE ->
+            _menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState9
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState9) : 'freshtv16)
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv17 * _menhir_state) = Obj.magic _menhir_stack in
+        ((let (_menhir_stack, _menhir_s) = _menhir_stack in
+        _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv18)
+
+and _menhir_discard : _menhir_env -> _menhir_env =
+  fun _menhir_env ->
+    let lexer = _menhir_env._menhir_lexer in
+    let lexbuf = _menhir_env._menhir_lexbuf in
+    let _tok = lexer lexbuf in
+    {
+      _menhir_lexer = lexer;
+      _menhir_lexbuf = lexbuf;
+      _menhir_token = _tok;
+      _menhir_error = false;
+    }
+
+and fichier : (Lexing.lexbuf -> token) -> Lexing.lexbuf -> (
+# 21 "parserProcessus.mly"
+      (unit)
+# 858 "parserProcessus.ml"
+) =
+  fun lexer lexbuf ->
+    let _menhir_env =
+      let (lexer : Lexing.lexbuf -> token) = lexer in
+      let (lexbuf : Lexing.lexbuf) = lexbuf in
+      ((let _tok = Obj.magic () in
+      {
+        _menhir_lexer = lexer;
+        _menhir_lexbuf = lexbuf;
+        _menhir_token = _tok;
+        _menhir_error = false;
+      }) : _menhir_env)
+    in
+    Obj.magic (let (_menhir_env : _menhir_env) = _menhir_env in
+    let (_menhir_stack : 'freshtv13) = ((), _menhir_env._menhir_lexbuf.Lexing.lex_curr_p) in
+    ((let _menhir_env = _menhir_discard _menhir_env in
+    let _tok = _menhir_env._menhir_token in
+    match _tok with
+    | PROCESS ->
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv9) = Obj.magic _menhir_stack in
+        ((let _menhir_env = _menhir_discard _menhir_env in
+        let _tok = _menhir_env._menhir_token in
+        match _tok with
+        | IDENTIFIER _v ->
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv5) = Obj.magic _menhir_stack in
+            let (_v : (
+# 16 "parserProcessus.mly"
+       (string)
+# 889 "parserProcessus.ml"
+            )) = _v in
+            ((let _menhir_stack = (_menhir_stack, _v) in
+            let _menhir_env = _menhir_discard _menhir_env in
+            let _tok = _menhir_env._menhir_token in
+            match _tok with
+            | LEFT_BRACE ->
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : ('freshtv1) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 900 "parserProcessus.ml"
+                )) = Obj.magic _menhir_stack in
+                ((let _menhir_env = _menhir_discard _menhir_env in
+                let _tok = _menhir_env._menhir_token in
+                match _tok with
+                | ACTIVITY ->
+                    _menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState3
+                | RESOURCE ->
+                    _menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState3
+                | RIGHT_BRACE ->
+                    _menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState3
+                | _ ->
+                    assert (not _menhir_env._menhir_error);
+                    _menhir_env._menhir_error <- true;
+                    _menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState3) : 'freshtv2)
+            | _ ->
+                assert (not _menhir_env._menhir_error);
+                _menhir_env._menhir_error <- true;
+                let (_menhir_env : _menhir_env) = _menhir_env in
+                let (_menhir_stack : ('freshtv3) * (
+# 16 "parserProcessus.mly"
+       (string)
+# 922 "parserProcessus.ml"
+                )) = Obj.magic _menhir_stack in
+                (raise _eRR : 'freshtv4)) : 'freshtv6)
+        | _ ->
+            assert (not _menhir_env._menhir_error);
+            _menhir_env._menhir_error <- true;
+            let (_menhir_env : _menhir_env) = _menhir_env in
+            let (_menhir_stack : 'freshtv7) = Obj.magic _menhir_stack in
+            (raise _eRR : 'freshtv8)) : 'freshtv10)
+    | _ ->
+        assert (not _menhir_env._menhir_error);
+        _menhir_env._menhir_error <- true;
+        let (_menhir_env : _menhir_env) = _menhir_env in
+        let (_menhir_stack : 'freshtv11) = Obj.magic _menhir_stack in
+        (raise _eRR : 'freshtv12)) : 'freshtv14))
+
+# 57 "parserProcessus.mly"
+  
+
+# 941 "parserProcessus.ml"
+
+# 269 "<standard.mly>"
+  
+
+# 946 "parserProcessus.ml"
diff --git a/TP8-9/process-analysis/parserProcessus.mli b/TP8-9/process-analysis/parserProcessus.mli
new file mode 100755
index 0000000..a3f43f8
--- /dev/null
+++ b/TP8-9/process-analysis/parserProcessus.mli
@@ -0,0 +1,27 @@
+
+(* The type of tokens. *)
+
+type token = 
+  | STARTS
+  | STARTED
+  | RIGHT_BRACE
+  | RESOURCE
+  | REQUIRES
+  | PROCESS
+  | NUMBER of (int)
+  | LEFT_BRACE
+  | IF
+  | IDENTIFIER of (string)
+  | FINISHES
+  | FINISHED
+  | END
+  | AMOUNT
+  | ACTIVITY
+
+(* This exception is raised by the monolithic API functions. *)
+
+exception Error
+
+(* The monolithic API. *)
+
+val fichier: (Lexing.lexbuf -> token) -> Lexing.lexbuf -> (unit)
diff --git a/TP8-9/process-analysis/parserProcessus.mly b/TP8-9/process-analysis/parserProcessus.mly
new file mode 100755
index 0000000..9d27471
--- /dev/null
+++ b/TP8-9/process-analysis/parserProcessus.mly
@@ -0,0 +1,57 @@
+%{
+
+(* Partie recopiee dans le fichier CaML genere. *)
+(* Ouverture de modules exploites dans les actions *)
+(* Declarations de types, de constantes, de fonctions, d'exceptions exploites dans les actions *)
+
+%}
+
+/* Declaration des unites lexicales et de leur type si une valeur particuliere leur est associee */
+
+%token PROCESS ACTIVITY STARTS FINISHES IF STARTED FINISHED
+%token RESOURCE AMOUNT REQUIRES
+%token LEFT_BRACE RIGHT_BRACE
+/* Defini le type des donnees associees a l'unite lexicale */
+%token <int> NUMBER
+%token <string> IDENTIFIER
+/* Unite lexicale particuliere qui represente la fin du fichier */
+%token END
+
+/* Type renvoye pour le nom terminal fichier */
+%type <unit> fichier
+
+/* Le non terminal fichier est l'axiome */
+%start fichier
+
+%% /* Regles de productions */
+
+fichier : processus END { (print_endline "fichier : processus END") }
+
+processus : PROCESS IDENTIFIER LEFT_BRACE elements RIGHT_BRACE { (print_endline "processus : process IDENTIFIER { elements }") }
+
+elements : /* Lambda, mot vide */ { (print_endline "elements : /* Lambda, mot vide */") }
+              | element elements { (print_endline "elements : element elements") }
+
+element : activite { (print_endline "element : activite") }
+	    | resource { (print_endline "element : resource") }
+
+resource : RESOURCE IDENTIFIER AMOUNT NUMBER { (print_endline "resource : resource IDENTIFIER amount NUMBER") }
+
+activite : ACTIVITY IDENTIFIER contraintes { (print_endline "activite : activity IDENTIFIER contraintes") }
+
+contraintes : /* Lambda, mot vide */ { (print_endline "contraintes : /* Lambda, mot vide */") }
+              | requires contraintes  { (print_endline "contraintes : requires contraintes") }
+              | contrainte contraintes { (print_endline "contraintes : contrainte contraintes") }
+              | LEFT_BRACE elements RIGHT_BRACE contraintes { (print_endline "contraintes : { elements } contraintes") }
+
+requires : REQUIRES NUMBER IDENTIFIER { (print_endline "requires : requires NUMBER IDENTIFIER") }
+
+contrainte : action IF IDENTIFIER etat { (print_endline "contrainte : action if IDENTIFIER etat") }
+
+action : STARTS { (print_endline "action : STARTS") }
+         | FINISHES { (print_endline "action : FINISHES") }
+
+etat : STARTED { (print_endline "etat : STARTED") }
+         | FINISHED { (print_endline "etat : FINISHED") }
+
+%%
diff --git a/TP8-9/process-analysis/tests/test00.processus b/TP8-9/process-analysis/tests/test00.processus
new file mode 100755
index 0000000..5ad4150
--- /dev/null
+++ b/TP8-9/process-analysis/tests/test00.processus
@@ -0,0 +1,8 @@
+/* Un premier exemple de processus */
+process ABC {
+   activity A 
+   activity B
+   activity C 
+      starts if A started
+      finishes if B finished
+}
\ No newline at end of file
diff --git a/TP8-9/process-analysis/tests/test01.processus b/TP8-9/process-analysis/tests/test01.processus
new file mode 100755
index 0000000..27c76ff
--- /dev/null
+++ b/TP8-9/process-analysis/tests/test01.processus
@@ -0,0 +1,11 @@
+/* Un deuxième exemple de processus avec des ressources */
+process ABC {
+   resource R amount 5
+   activity A 
+     requires 2 R
+   activity B
+   activity C 
+      requires 3 R
+      starts if A started
+      finishes if B finished
+}
diff --git a/TP8-9/process-analysis/tests/test02.processus b/TP8-9/process-analysis/tests/test02.processus
new file mode 100755
index 0000000..fda1aa3
--- /dev/null
+++ b/TP8-9/process-analysis/tests/test02.processus
@@ -0,0 +1,18 @@
+/* Un troisième exemple de processus hiérarchique avec des ressources */
+process ABC {
+   resource R amount 5
+   activity A {
+      activity A1 {
+         activity A11
+      }   
+         requires 1 R
+      activity A2
+         requires 2 R
+         starts if A1 finished
+   }
+      requires 2 R
+   activity B
+   activity C requires 3 R
+      starts if A started
+      finishes if B finished
+}
\ No newline at end of file