23 lines
637 B
Plaintext
23 lines
637 B
Plaintext
|
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
|