proposition: Lemma pdfs_uniq s l x : uniq l -> {subset l <= ~: s} -> uniq (pdfs (s,l) x).2.
proof: Proof. move=> uniql subls. have := pdfs_correct (s,l) x (conj uniql subls). case: (pdfs _ _) => s' l' /=. by have [_ [[]]//| _ [_ ->]] /= := boolP (x \in s). Qed.
imports: mathcomp(all_ssreflect) extra