proposition: Lemma injectivePn : reflect (exists x, exists2 y, x != y & f x = f y) (~~ injectiveb).
proof: Proof. apply: (iffP (dinjectivePn _)) => [[x _ [y nxy eqfxy]] | [x [y nxy eqfxy]]]; by exists x => //; exists y => //; rewrite inE /= andbT eq_sym in nxy *. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)