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(* 02110-1301 USA                                                     *)
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(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
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(*                                                                           *)
(*          InterChange Law                                                  *)
(*                                                                           *)
(*          Ge'rard Huet and Amokrane Saibi,  June 1994                      *)
(*                                                                           *)
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Require Export CatFunct.
Set Implicit Arguments.
Unset Strict Implicit.
Section horz_comp.
Variables (A B C : Category) (F G : Functor A B) (F' G' : Functor B C)
(T : NT F G) (T' : NT F' G').
Definition Ast (a : A) : (F o_F F') a --> (G o_F G') a :=
T' (F a) o FMor G' (T a).

(* Specifications: *)
Lemma Ast_eq :
forall a : A, FMor F' (T a) o T' (G a) =_S T' (F a) o FMor G' (T a).
Lemma Ast_nt_law : NT_law Ast.
Canonical Structure CompH_NT := Build_NT Ast_nt_law.