Definition composePathOverPath {X:Type} {x x':X} {p:x=x'} {Y : X -> Type} {y : Y x} {y' y'' : Y x'} : PathOver p y y' → y' = y'' → PathOver p y y''. Proof. intros q e. now induction e. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.