proposition: Lemma RmsuS_prod x y : inc x BRms -> inc y BRms -> inc (x *r y) BRps.
proof: Proof. move => sa sb. move:(BRopp_negative1 sa)(BRopp_negative1 sb) => sc sd. rewrite /BRprod (Y_false (BRms_nz sa)) (Y_false (BR_di_neg_spos sa)). rewrite /BRprod (Y_false (BRms_nz sb)) (Y_false (BR_di_neg_spos sb)). rewrite - (BR_prod_aux1 sc sd); apply:(RpsS_prod sc sd). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)