Lemma truncminus_le_r : ∏ k x y : X, Lle lat x y → Lle lat (truncminus ex x k) (truncminus ex y k). Proof. intros k x y <-. eapply rcancel. { apply is1. } simpl. rewrite is3, 2!istruncminus_ex. rewrite is4, isassoc_Lmin, Lmin_id. rewrite <- is4. apply pathsinv0, istruncminus_ex. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.