proposition: Lemma up_Int_part r : (up r = Int_part r + 1)%Z.
proof: Proof. case: (base_Int_part r) => H1 H2. rewrite -(up_tech r (Int_part r)) // plus_IZR //; 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)