Section natiso_def.
Variable A B : Category.
Definition RNatIso_law (F G : Functor A B) (T : NT F G)
(T1 : NT G F) := T1 o_NTv T =_NT Id_CatFunct G.
Variable F G : Functor A B.
Definition AreNatIsos (T : NT F G) (T1 : NT G F) :=
RNatIso_law T T1 /\ RNatIso_law T1 T.
Structure > NatIso : Type :=
{NatIso_mor :> NT F G;
NatIso_inv : NT G F;
Prf_NatIso :> AreNatIsos NatIso_mor NatIso_inv}.

Lemma Idr_nat_inv :
forall i : NatIso, RNatIso_law (NatIso_inv i) (NatIso_mor i).