proposition: Lemma apply_equiv_dom {A B} (P : B -> Type) (e : Equiv A B) : (forall x : A, P (equiv e x)) -> forall x : B, P x.
proof: Proof. intros. specialize (X (e ^-1 x)). rewrite inv_equiv_equiv in X. exact X. Defined.
imports: Equations Utf8 DepElimDec EqDecInstances