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.

(* Specifications: *)
Lemma beq_float_dec_true a b : beq_float_dec a b = true -> a = b.
intros.  unfold beq_float_dec in *. destruct (Float.eq_dec a b); congruence.