proposition: Lemma exists_eq_inP D f1 f2 : reflect (exists2 x, D x & f1 x = f2 x) [exists (x | D x), f1 x == f2 x].
proof: Proof. exact: (exists_inPP _ (fun=> eqP)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)