Module Inverse21 := Inverse N2 N1.
Local Notation h12 := Hom12.natural_isomorphism.
Local Notation h21 := Hom21.natural_isomorphism.
Definition isomorphism (f1 : N1.t -> N2.t) (f2 : N2.t -> N1.t) : Prop :=
Hom12.homomorphism f1 /\ Hom21.homomorphism f2 /\
forall n, N1.eq (f2 (f1 n)) n /\
forall n, N2.eq (f1 (f2 n)) n.

Theorem iso_nat_iso : isomorphism h12 h21.