proposition: Lemma real_lteifNE x y C : x \is Num.real -> y \is Num.real -> x < y ?<= if ~~ C = ~~ (y < x ?<= if C).
proof: Proof. by move=> ? ?; rewrite comparable_lteifNE ?real_comparable. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)