Definition apsetwithbinop_setwithbinop : apsetwithbinop → setwithbinop := λ X : apsetwithbinop, (apSet_pr1 (apsetwithbinop_pr1 X)),, (pr1 (pr2 X)).
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.DecidablePropositions.