proposition: Lemma floorP (r : R) : r - 1 < IZR (floor r) <= r.
proof: Proof. rewrite /floor; case: (base_Int_part r) => ? ?; split=> //; Lra.lra. Qed.
imports: mathcomp(all_ssreflect) mathcomp(all_algebra vector reals normedtype) mathcomp(mathcomp_extra boolp) mathcomp(Rstruct) ssrR realType_ext Reals Lra mathcomp(lra)