proposition: Lemma BRprod_nz x y: realp x -> realp y -> x <> \0r -> y <> \0r -> x *r y <> \0r.
proof: Proof. move => xr yr xnz ynz. case/BR_i1P: xr => //;case/BR_i1P: yr => // sb sa. + by move :(RpsS_prod sa sb) => /BRps_iP []. + by move :(RpmsS_prod sa sb) => /BRms_iP []. + rewrite BRprodC; by move :(RpmsS_prod sb sa) => /BRms_iP []. + by move :(RmsuS_prod sa sb) => /BRps_iP []. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)