Notation "x ≤ y ≤ z" := (x ≤ y ∧ y ≤ z) (at level 70, y at next level).
Notation "x < y ≤ z" := (x < y ∧ y ≤ z) (at level 70, y at next level).
Notation "x ≤ y < z" := (x ≤ y ∧ y < z) (at level 70, y at next level).
Infix "∈" := In (at level 70).
(* Compatibilité 8.4 *)
Infix "=?" := beq_nat (at level 70, no associativity).
Obligation Tactic := idtac.
Scheme Equality for prod.
Scheme Equality for list.
Set Implicit Arguments.
Section Trivial.

Lemma list_beq_eq A
(A_beq : A -> A -> bool) l1 l2 (A_beq_eq : forall a1 a2, In a1 l1 -> In a2 l2 -> (A_beq a1 a2 = true <-> a1 = a2)) :
list_beq _ A_beq l1 l2 = true <-> l1 = l2.