Record union_th3_property (Y : Ens) : Prop := 
  {union_th3_property_in_the_union : IN Y U;
   union_th3_property_not_equal_X : ~ EQ X Y}.Record union_th3_property (Y : Ens) : Prop := 
  {union_th3_property_in_the_union : IN Y U;
   union_th3_property_not_equal_X : ~ EQ X Y}.Record union_th3_property (Y : Ens) : Prop := 
  {union_th3_property_in_the_union : IN Y U;
   union_th3_property_not_equal_X : ~ EQ X Y}.Definition A_sub_V_proof1_Out : False := h step1_1.

Lemma A_sub_V_proof_Out : IN Z V.