#[global]
Hint Extern 1 (false <> true) => exact diff_false_true : core.

(* Specifications: *)
Lemma eq_true_false_abs : forall b:bool, b = true -> b = false -> False.
Lemma not_true_is_false : forall b:bool, b <> true -> b = false.
Lemma not_false_is_true : forall b:bool, b <> false -> b = true.
Lemma not_true_iff_false : forall b, b <> true <-> b = false.
Lemma not_false_iff_true : forall b, b <> false <-> b = true.
#[ local ] Definition le (b1 b2:bool) :=
match b1 with
| true => b2 = true
| false => True
end.