proposition: Lemma cardID B A : #|[predI A & B]| + #|[predD A & B]| = #|A|.
proof: Proof. rewrite -cardUI addnC [#|predI _ _|]eq_card0 => [|x] /=. by apply: eq_card => x; rewrite !inE andbC -andb_orl orbN. by rewrite !inE -!andbA andbC andbA andbN. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)