proposition: Lemma subCset_P3 A B C : sub A (B -s C) <-> (sub A B /\ disjoint A C).
proof: Proof. split => [h | [sab dac t ta]]. by split; [move => t ta | apply: disjoint_pr => t ta]; case /setC_P: (h _ ta). apply/setC_P; split; [by apply: sab | move => tC; empty_tac1 t]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)