proposition: Lemma identity_composition_right (M : Metacategory) : ∀ f g fg u, identity M u -> composite M f g fg -> defined g u (pairs M) -> defined fg u (pairs M).
proof: Proof. intros. destruct H as [c _]. apply composite_defined with (h:=fg); auto; try solve [ apply c ]. Qed.
imports: Coq.Structures.DecidableTypeEx Coq.FSets.FMapFacts Category.Lib.FMapExt Coq.Arith.PeanoNat Category.Lib Category.Theory.Category