Show stronger soundness in Error validator

coq/Expressions.v

@@ -394,19 +394,18 @@ For each evaluation of using an arbitrary epsilon, we can replace it by
 evaluating the subexpressions and then binding the result values to different
 variables in the Environment.
  **)
-Lemma binary_unfolding b f1 f2 E v1 v2 m1 m2 Gamma:
+Lemma binary_unfolding b f1 f2 E v1 v2 m1 m2 Gamma delta:
   (b = Div -> ~(v2 = 0 )%R) ->
+  (Rabs delta <= Q2R (mTypeToQ (join m1 m2)))%R ->
   eval_exp E Gamma f1 v1 m1 ->
   eval_exp E Gamma f2 v2 m2 ->
-  eval_exp E Gamma (Binop b f1 f2) (perturb (evalBinop b v1 v2) (Q2R (mTypeToQ (join m1 m2)))) (join m1 m2) ->
+  eval_exp E Gamma (Binop b f1 f2) (perturb (evalBinop b v1 v2) delta) (join m1 m2) ->
   eval_exp (updEnv 2 v2 (updEnv 1 v1 emptyEnv))
            (updDefVars 2 m2 (updDefVars 1 m1 Gamma))
-             (Binop b (Var R 1) (Var R 2)) (perturb (evalBinop b v1 v2) (Q2R (mTypeToQ (join m1 m2)))) (join m1 m2).
+             (Binop b (Var R 1) (Var R 2)) (perturb (evalBinop b v1 v2) delta) (join m1 m2).
 Proof.
   intros no_div_zero eval_f1 eval_f2 eval_float.
   econstructor; try auto.
-  rewrite Rabs_right; try lra.
-  auto using Rle_ge, mTypeToQ_pos_R.
 Qed.
 
 (*