proposition: Lemma Rmorph_inv x : phi x^-1 == (phi x)^-1.
proof: Proof. have phi_Proper := Rmorph_Proper phiP. case: (x : RR)^-1 / IFR_cases => _ [][x0 ->]; first by rewrite x0 !phi0 invR0. by rewrite phiV ?invRE //; apply: Rmorph_neq0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq order) mathcomp(ssralg ssrnum ssrint rat) Coq(Morphisms Setoid) fourcolor(real realsyntax realprop)