+
+Lemma isos_forward_equal_then_backward_equal `{C:Category}{a}{b}(i1 i2:a ≅ b) : #i1 ~~ #i2 -> #i1⁻¹ ~~ #i2⁻¹.
+ intro H.
+ setoid_rewrite <- left_identity at 1.
+ setoid_rewrite <- (iso_comp2 i2).
+ setoid_rewrite associativity.
+ setoid_rewrite <- H.
+ setoid_rewrite iso_comp1.
+ setoid_rewrite right_identity.
+ reflexivity.
+ Qed.
+
+Lemma iso_inv_inv `{C:Category}{a}{b}(i:a ≅ b) : #(i⁻¹)⁻¹ ~~ #i.
+ unfold iso_inv; simpl.
+ reflexivity.
+ Qed.