Section UNION.
Variable f : nat -> ensemble (frm L).
Definition union_f : ensemble (frm L) :=
fun p => exists n, p \in f n.
Hypothesis incl : forall n1 : nat, forall n2 : nat, forall LE : n1 <= n2, f n1 \subseteq f n2.
Hypothesis equiconsistent : forall n : nat, inconsistent (f n) <-> inconsistent (f (S n)).

Lemma equiconsistent_union_f
: inconsistent (f 0) <-> inconsistent union_f.