Module Hom12 := Homomorphism N1 N2.Module Hom21 := Homomorphism N2 N1.Module Inverse12 := Inverse N1 N2.Module Inverse21 := Inverse N2 N1.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.