proposition: Lemma card_le1_eqP A : reflect {in A &, forall x, all_equal_to x} (#|A| <= 1).
proof: Proof. apply: (iffP card_le1P) => [Ale1 x y xA yA /=|all_eq x xA y]. by apply/eqP; rewrite -[_ == _]/(y \in pred1 x) -Ale1. by rewrite inE; case: (altP (y =P x)) => [->//|]; exact/contra_neqF/all_eq. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)