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(** *        Rmax              *)
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Definition Rmax (x y:R) : R :=
  match Rle_dec x y with
    | left _ => y
    | right _ => x
  end.

Lemma Rmax_Rle : forall r1 r2 r, r <= Rmax r1 r2 <-> r <= r1 \/ r <= r2.