proposition: Lemma pPos: (0 <= p)%R.
proof: Proof. unfold FtoRradix; apply RleRoundedR0 with b t (Closest b radix) (x * (powerRZ radix s + 1))%R; auto with zarith. apply ClosestRoundedModeP with t; auto with zarith. apply Rmult_le_pos; auto with real. apply Rplus_le_le_0_compat; auto with real. apply powerRZ_le, IZR_lt; lia. Qed.
imports: Reals ZArith List PeanoNat Psatz