Definition beq_int (i1 i2 : Integers.int) : bool :=
Zbool.Zeq_bool (Int.intval i1) (Int.intval i2).
Hint Resolve beq_int_true : expr_beq.
Hint Resolve beq_int_refl : expr_beq.
Hint Rewrite beq_int_refl : expr_beq.
Definition beq_long (i1 i2 : int64) : bool :=
Zeq_bool (Int64.intval i1) (Int64.intval i2).
Hint Resolve beq_long_refl : expr_beq.
Hint Rewrite beq_long_refl : expr_beq.
Hint Resolve beq_long_true : expr_beq.
Definition beq_float_dec a b:= if Float.eq_dec a b then true else false.
intros.  unfold beq_float_dec in *. destruct (Float.eq_dec a b); congruence.
Qed. (*If things are slow, this may be the culprit *)
Hint Resolve beq_float_refl : expr_beq.
Hint Rewrite beq_float_refl : expr_beq.
Hint Resolve beq_float_dec_true : expr_beq.
Definition beq_float32_dec a b:= if Float32.eq_dec a b then true else false.

Lemma beq_float32_dec_true a b : beq_float32_dec a b = true -> a = b.