fact: Definition IsInitialMorphism_property_morphism_unique (M : IsInitialMorphism Ap) (Y : D) (f : morphism C X (U Y)) m' (H : U _1 m' o IsInitialMorphism_morphism M = f) : IsInitialMorphism_property_morphism M Y f = m' := ap (@CommaCategory.h _ _ _ _ _ _ _) (@contr _ (M (CommaCategory.Build_object !X U tt Y f)) (CommaCategory.Build_morphism Ap (CommaCategory.Build_object !X U tt Y f) tt m' (H @ (right_identity _ _ _ _)^)%path)).
imports: Category.Core Functor.Core Category.Dual Functor.Dual Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Trunc Types.Sigma HoTT.Tactics Basics.Tactics