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.

Lemma test_simpl_left_right_3 : forall a b c, a+(b+c) = (c+b)+a.