Section nothing_strictsub_Zero.
Variable X : Ens.
Hypothesis h : StrictSUB X Zero.
Let step1 : SUB X Zero.
Proof StrictSUB_sub X Zero h.
Let step2 : Its_empty X.
Proof fun (Y : Ens) (m : IN Y X) => EmptySet_th1 Y (step1 Y m).
Let step3 : EQ X Zero.
Proof its_empty_implies_equals_emptyset X step2.
Definition nothing_strictsub_Zero_Out : False := StrictSUB_neq X Zero h step3.
End nothing_strictsub_Zero.

Theorem Nothing_strictsub_Zero : forall X : Ens, ~ StrictSUB X Zero.