proposition: Lemma disjoint_id `{laws} `{AL+BOT ≪ l} n m (p q: X n m): p ⊓ q ≦ 0 -> 1 ⊓ (p⋅q°) ≡ 0.
proof: Proof. intro Hpq. apply leq_xb_iff. rewrite capC, capxdot. ra_normalise. rewrite Hpq. ra. Qed.
imports: common lattice monoid kleene normalisation rewriting