(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.
Require Import Category.Core Functor.Core. Require Import Category.Dual Functor.Dual. Require Import Category.Objects. Require Import InitialTerminalCategory.Core InitialTerminalCategory.Functors. Import Comma.Core. Require Import Trunc Types.Sigma HoTT.Tactics. Require Import Basics.Tactics.