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).

(* Specifications: *)
Lemma S_is_suc n: S n = n+1.
Lemma or_idem: ∀ A, A ↔ A ∨ A.
Lemma and_idem: ∀ A, A ↔ A ∧ A.
Lemma and_left: ∀ A B, A ∧ B → A.
Lemma or_false_idem: ∀ A, A ↔ A ∨ False.