proposition: Lemma alt_Build_Bijective `{Equiv A} `{Equiv B} (f : A → B) `{!Inverse f} : Setoid_Morphism f → Setoid_Morphism (f⁻¹) → f⁻¹ ∘ f = id → f ∘ f⁻¹ = id → Bijective f.
proof: Proof. intros. split. now apply (alt_Build_Injective f). split; auto. Qed.
imports: MathClasses.theory.setoids MathClasses.interfaces.abstract_algebra