Definition PathOverToPathPair {X:Type} {x x':X} (p:x=x') {Y : X -> Type} (y : Y x) (y' : Y x') : PathOver p y y' → PathPair (x,,y) (x',,y'). Proof. intros q. induction p. exists (idpath x). cbn. exact q. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.