proposition: Theorem EvenClosestMonotone2: forall (p q : R) (p' q' : float), (p <= q)%R -> (EvenClosest bo radix precision p p') -> (EvenClosest bo radix precision q q') -> (p' <= q')%R.
proof: Proof. intros. case H; intros H2. generalize EvenClosestMonotone; unfold MonotoneP. intros W; unfold FtoRradix. apply W with bo precision p0 q0; auto. generalize EvenClosestUniqueP; unfold UniqueP. intros W; unfold FtoRradix. right; apply W with bo precision p0; auto with real. rewrite H2; auto. Qed.
imports: Reals ZArith List PeanoNat Psatz