proposition: Lemma FieldInDg_rac_EqualSets: forall p h s1 f dg, Rac2.FieldInDg_rac p h s1 f dg -> forall s2, s1 [=] s2 -> Rac2.FieldInDg_rac p h s2 f dg.
proof: Proof. intros p h s1 f dg H. induction H; intros. apply Rac2.FieldInDg_rac_step with dg'. apply IHFieldInDg_rac1; trivial. apply IHFieldInDg_rac2; trivial. apply Rac2.FieldInDg_rac_static; trivial. apply Rac2.FieldInDg_rac_dynamic with pivot; trivial. intro. elim H0. apply H1; trivial. apply Rac2.FieldInDg_rac_same; trivial. Qed.
imports: Coq(List) JML(Stack) Coq(ListSet) Coq(Bool) Coq(ZArith) Coq(Relation_Operators) JML(ListHelpers) Coq(Classical) Coq(DecidableType) Coq(FSetInterface) Coq(FSetProperties) Coq(FSetEqProperties) Coq(FSetFacts) Coq(Sumbool) Coq(Lia)