Definition latticewithgt_weq {X Y : hSet} (H : weq Y X) (lat : latticewithgt X) : latticewithgt Y. Proof. exists (lattice_weq H lat), (StrongOrder_bck H (Lgt lat)). apply islatticewithgtrel_weq. apply (pr2 (pr2 lat)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.