intros p q r H' H'0; apply Rle_antisym.
elim H'0; intros H'1 H'2; elim H'2; intros H'3 H'4; apply H'4; clear H'2 H'0;
auto.
case H'; auto.
apply isMin_inv1 with (1 := H'); auto.
elim H'; intros H'1 H'2; elim H'2; intros H'3 H'4; apply H'4; clear H'2 H';
auto.
case H'0; auto.
apply isMin_inv1 with (1 := H'0); auto.
Qed.
(* Maximum is defined upto equality *)

Theorem MaxEq :
forall (p q : float) (r : R), isMax r p -> isMax r q -> p = q :>R.