+lemma memb_hd: ∀S,a,l. memb S a (a::l) = true.
+#S #a #l normalize >(proj2 … (eqb_true S …) (refl S a)) //
+qed.
+
+lemma memb_cons: ∀S,a,b,l.
+ memb S a l = true → memb S a (b::l) = true.
+#S #a #b #l normalize cases (a==b) normalize //
+qed.
+
+lemma memb_single: ∀S,a,x. memb S a [x] = true → a = x.
+#S #a #x normalize cases (true_or_false … (a==x)) #H
+ [#_ >(\P H) // |>H normalize #abs @False_ind /2/]
+qed.
+