fact: Definition composite_defined (M : Metacategory) (f g h : arr M) : composite M f g h → defined f g (pairs M) := fun H => proj2 (@in_mapsto_iff _ _ _) (ex_intro _ h H).
imports: Coq.Structures.DecidableTypeEx Coq.FSets.FMapFacts Category.Lib.FMapExt Coq.Arith.PeanoNat Category.Lib Category.Theory.Category