Section norm_trans.
Variables (A B C D : {set gT}).
Hypotheses (nBA : A \subset 'N(B)) (nCA : A \subset 'N(C)).
End norm_trans.

Lemma norms_bigcup I r (P : pred I) A (B_ : I -> {set gT}) :
A \subset \bigcap_(i <- r | P i) 'N(B_ i) ->
A \subset 'N(\bigcup_(i <- r | P i) B_ i).