intros p q H' H'0.
apply floatEq; auto.
apply eq_IZR; auto.
apply Rmult_eq_reg_l with (r := powerRZ radix (Fexp p));
auto with real zarith.
repeat rewrite (Rmult_comm (powerRZ radix (Fexp p)));
pattern (Fexp p) at 2 in |- *; rewrite H'0; auto with real zarith.
Qed.

Theorem Rlt_Float_Zlt :
forall p q r : Z, (Float p r < Float q r)%R -> (p < q)%Z.