proposition: Lemma disjoint_vect_iff' `{AL+DIV+BOT+TOP ≪ l} {n m} {p q: X n m} {Hq: is_vector q}: p ⊓ q ≦ 0 <-> q°⋅p ≦ 0.
proof: Proof. split; intro Hpq. rewrite <-capxt, capdotx, cnv_invol, vector, Hpq. ra. rewrite <-ldv_spec in Hpq. rewrite capC, Hpq. rewrite <-vector at 1. rewrite capdotx. rewrite ldv_cancel. ra. Qed.
imports: common lattice monoid kleene normalisation rewriting