Definition homotinvweqweq_comp_3 {X} {P:X->Type} (irr:∏ x (p q:P x), p = q) (sec:∏ x, P x) (x:X) (p:P x) : let f := weqpr1_irr_sec irr sec in let g := invweqpr1_irr_sec irr sec in let w := x,,p in let w' := g x in @paths (w' = w) (homotweqinvweq g w) (maponpaths _ (irr x (sec x) (pr2 w))). Proof. reflexivity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Equivalences.