Section Naturals_th1_proof.
Variable X : Ens.
Hypothesis h : Contains_NN X.
Variable B : Ens.
Hypothesis k : IN B Naturals.
Let step1 : Element_of_NN B := Naturals_pr2 B k.
Definition Naturals_th1_proof_Out : IN B X := step1 X h.
End Naturals_th1_proof.

Theorem Naturals_th1 : forall (X : Ens) (h : Contains_NN X), SUB Naturals X.