fact: Definition IsInitialMorphism_property (M : IsInitialMorphism Ap) (Y : D) (f : morphism C X (U Y)) : Contr { m : morphism D (IsInitialMorphism_object M) Y | U _1 m o IsInitialMorphism_morphism M = f } := Build_Contr _ (IsInitialMorphism_property_morphism M Y f; IsInitialMorphism_property_morphism_property M Y f) (fun m' => path_sigma _ (IsInitialMorphism_property_morphism M Y f; IsInitialMorphism_property_morphism_property M Y f) m' (@IsInitialMorphism_property_morphism_unique M Y f m'.1 m'.2) (center _)).
imports: Category.Core Functor.Core Category.Dual Functor.Dual Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Trunc Types.Sigma HoTT.Tactics Basics.Tactics