Section cone_nt.
Variable T : forall a : J, c --> F a.
Definition Cone_law :=
forall (i j : J) (g : i --> j), T j =_S T i o FMor F g.
Coercion Prf_Cone_nt_law : Cone_law >-> NT_law.
Variable p : Cone_law.
Canonical Structure Build_Cone : Cone := Build_NT (Prf_Cone_nt_law p).
End cone_nt.
Coercion Build_Cone : Cone_law >-> Cone.
(*** rewrite rules ***)

Lemma EqC :
forall (tau : Cone) (i j : J) (g : i --> j), tau j =_S tau i o FMor F g.