proposition: Theorem MaxEx : forall r : R, exists max : float, isMax r max.
proof: Proof. intros r; case (MinEx r). intros x H'. case (Req_dec x r); intros H'1. exists x. rewrite <- H'1. red in |- *; split; [ case H' | split ]; auto with real. exists (FNSucc b radix precision x). apply MinMax; auto. Qed.
imports: Reals ZArith List PeanoNat Psatz