proposition: Lemma ratRM a1 a2 : (a1 * a2)%R == a1 * a2.
proof: Proof. have [[r1 {2}-> Dr1] [r2 {2}-> Dr2]] := (ratR_eq a1, ratR_eq a2). apply/(pmulIR (ltR0Sn r1.2))/(pmulIR (ltR0Sn r2.2)). rewrite -2!ratRMn (mulRAC a1) -mulRA {}Dr1 {}Dr2 -mulrA mulrACA. by rewrite !divfK ?intr_eq0 // -intrM ratRz intRM. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)