Definition switch_weq {X Y} (f:X ≃ Y) {x y} : y = f x -> invweq f y = x. Proof. intros p. exact (maponpaths (invweq f) p @ homotinvweqweq f x). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.PartA.