Lemma PathOverUniqueness {X:Type} {x x':X} (p:x=x') {Y : X -> Type} (y : Y x) : ∃! (y' : Y x'), PathOver p y y'. Proof. induction p. apply iscontrcoconusfromt. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.