proposition: Lemma eq_existsb P1 P2 : P1 =1 P2 -> [exists x, P1 x] = [exists x, P2 x].
proof: Proof. by move=> eqP12; congr (_ != 0); apply: eq_card. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)