Ltac simpl_left_sym := 
  apply (f_equal2_sym Fplus Fplus_sym);[solve [ring] | idtac];idtac "simpl gauche sym".Ltac simpl_right_sym := 
  apply (f_equal2_sym Fplus Fplus_sym);[idtac | solve[ring]];idtac "simpl droite sym".Ltac simpl_left_right_sym := repeat (simpl_left_sym || simpl_right_sym).Ltac simpl_eq :=  simpl_left_right;simpl_left_right_sym.

(* Specifications: *)
Lemma eq_simpl_1 : forall a b c, b=c -> a+b = a+c .
Lemma eq_simpl_2 : forall a b c, b=c -> b+a = c+a .
Lemma eq_simpl_3 : forall a b c, b=c -> a+b = c+a .
Lemma eq_simpl_4 : forall a b c, b=c -> b+a = a+c .
Lemma eq_simpl_5 : forall a b c, b=c -> a*b = a*c .
Lemma eq_simpl_6 : forall a b c, b=c -> b*a = c*a .
Lemma eq_simpl_7 : forall a b c, b=c -> a*b = c*a .
Lemma eq_simpl_8 : forall a b c, b=c -> b/a = c/a .
Lemma eq_simpl_9 : forall b c, b=c -> -b = -c .
Lemma eq_simpl_10 : forall a b c, b=c -> a-b = a-c .
Lemma test_simpl_left_right_1 : forall a b c, (a)+(c+b) = (a+a-a)+(b+c).
Lemma test_simpl_left_right_2 : forall a b c, (c+b)+((a)+(c+b)) = (c+b)+ ((a+a-a)+(b+c)).
Lemma test_simpl_left_right_3 : forall a b c, a+(b+c) = (c+b)+a.