Section total_th1_proof.
Variable X F : Ens.
Hypothesis i : IN X F.
Let step1 : IN X (UnionPlus F).
Proof UnionPlus_th1 X F i.
Let step2 : IN X (UnionPlus (UnionPlus F)).
Proof UnionPlus_th1 X (UnionPlus F) step1.

Lemma total_th1_Out : IN X (Total F).