intros r1 r2 p q H' H'0 H'1 H'2; red in |- *.
inversion H'.
split.
apply (ClosestCompatible r1 r2 p q); auto.
case H0; intros H1.
left.
apply FNevenEq with (f1 := p); auto.
case H; auto.
right; intros q0 H'3.
unfold FtoRradix in |- *; rewrite <- H'1; auto.
apply H1; auto.
apply (ClosestCompatible r2 r1 q0 q0); auto.
case H'3; auto.
Qed.

(* Specifications: *)
Theorem EvenClosestMinOrMax : MinOrMaxP b radix EvenClosest.
red in |- *; intros r p H'; case (ClosestMinOrMax r p); auto.