proposition: Lemma prob_IZR_subproof (p : positive) : (0 <= / IZR (Zpos p) <= 1)%O.
proof: Proof. have [/RleP ? /RleP ?] : (0 <= / IZR (Zpos p) <= 1)%coqR. split; first exact/Rlt_le/Rinv_0_lt_compat/IZR_lt/Pos2Z.is_pos. rewrite -[X in (_ <= X)%coqR]Rinv_1; apply Rle_Rinv => //. - exact/IZR_lt/Pos2Z.is_pos. - exact/IZR_le/Pos2Z.pos_le_pos/Pos.le_1_l. exact/andP. Qed.
imports: mathcomp(all_ssreflect) mathcomp(all_algebra vector reals normedtype) mathcomp(mathcomp_extra boolp) mathcomp(Rstruct) ssrR realType_ext Reals Lra mathcomp(lra)