42 lines
572 B
Coq
Executable file
42 lines
572 B
Coq
Executable file
Require Import Naturelle.
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Section Session1_2020_Logique_Exercice_1.
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Variable A B C : Prop.
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Theorem Exercice_1_Naturelle : ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
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I_imp H1.
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I_imp H2.
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E_imp A.
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E_ou (A -> C) (B -> C).
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Hyp H1.
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trivial.
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I_imp H3.
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I_imp H4.
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E_imp B.
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Hyp H3.
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E_et_d A.
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Hyp H2.
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E_et_g B.
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Hyp H2.
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Qed.
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Theorem Exercice_1_Coq : ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
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intros.
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destruct H.
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destruct H0.
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cut A.
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exact H.
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exact H0.
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cut B.
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exact H.
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cut (A /\ B).
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intro H2.
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elim H2.
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intros HA HB.
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exact HB.
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exact H0.
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Qed.
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End Session1_2020_Logique_Exercice_1.
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