proposition: Lemma seq_double n: seq (double n) ≡ map (@set.xO _) (seq n) ++ map (@set.xI _) (seq n).
proof: Proof. induction n. reflexivity. simpl double. simpl seq. fold_cons. rewrite IHn. simpl map. rewrite 2map_app. rewrite 6map_map. rewrite set.xO_0, set.xI_0. setoid_rewrite set.xO_S. setoid_rewrite set.xI_S. simpl. refine (comm4 [_] [_] _ _). Qed.
imports: lattice lsyntax comparisons lset boolean sups