[ true ⇒ b2
| false ⇒ not_bool b2 ].
+lemma eqbool_to_eq : ∀b1,b2:bool.(eq_bool b1 b2 = true) → (b1 = b2).
+ unfold eq_bool;
+ intros;
+ elim b1 in H:(%);
+ elim b2 in H:(%);
+ normalize in H:(%);
+ try reflexivity;
+ destruct H.
+qed.
+
(* \ominus *)
notation "hvbox(⊖ a)" non associative with precedence 36
for @{ 'not_bool $a }.