proposition: Lemma prob_divRnnm_subproof n m : (R0 <= divRnnm n m <= R1)%O.
proof: Proof. apply/andP; split. by rewrite /divRnnm RdivE' divr_ge0// INRE ler0n. rewrite /divRnnm RdivE' !INRE. have [/eqP ->|n0] := boolP (n == O). by rewrite mul0r ler01. rewrite ler_pdivrMr// ?ltr0n ?addn_gt0; last first. by rewrite lt0n n0. by rewrite mul1r ler_nat leq_addr. Qed.
imports: mathcomp(all_ssreflect) mathcomp(all_algebra vector reals normedtype) mathcomp(mathcomp_extra boolp) mathcomp(Rstruct) ssrR realType_ext Reals Lra mathcomp(lra)