proposition: Lemma leR_pinv2 x y : x > 0 -> y > 0 -> (x^-1 <= y^-1 <-> y <= x).
proof: Proof. move=> xgt0 ygt0; rewrite -(leR_pmul2r _ _ xgt0). by rewrite -(leR_pmul2r _ _ ygt0) -!mulRA pmulKR // (mulRC x) pmulKR. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)