(*****  StrictSUB *****)


Record StrictSUB (A B : Ens) : Prop := 
  {StrictSUB_sub : SUB A B; StrictSUB_neq : ~ EQ A B}.(*****  StrictSUB *****)


Record StrictSUB (A B : Ens) : Prop := 
  {StrictSUB_sub : SUB A B; StrictSUB_neq : ~ EQ A B}.(*****  StrictSUB *****)


Record StrictSUB (A B : Ens) : Prop := 
  {StrictSUB_sub : SUB A B; StrictSUB_neq : ~ EQ A B}.

(* Specifications: *)
Lemma strictsub_trans1a_Out : False.
Lemma strictsub_trans1_Out : StrictSUB A C.
Theorem StrictSUB_trans1 : forall (A B C : Ens) (h : StrictSUB A B) (k : SUB B C), StrictSUB A C.
Lemma emptyset_empty_Out : False.
Theorem EmptySet_th1 : forall (X : Ens) (h : IN X EmptySet), False.
Lemma emptyset_subset_everything_2_Out : IN B A.
Lemma emptyset_subset_everything_Out : SUB EmptySet A.
Theorem EmptySet_th2 : forall A : Ens, SUB EmptySet A.