proposition: Lemma card_gt1P A : reflect (exists x y, [/\ x \in A, y \in A & x != y]) (1 < #|A|).
proof: Proof. apply: (iffP card_geqP) => [[s] []|[x] [y] [xA yA xDy]]. case: s => [|a [|b []]]//= /[!(inE, andbT)] aDb _ subD. by exists a, b; rewrite aDb !subD ?inE ?eqxx ?orbT. by exists [:: x; y]; rewrite /= !inE xDy; split=> // z /[!inE] /pred2P[]->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)