Section Infinite_sets.
Variable U : Type.
Variable V : Type.

Theorem Image_set_continuous :
forall (A:Ensemble U) (f:U -> V) (X:Ensemble V),
Finite V X ->
Included V X (Im U V A f) ->
exists n : _,
(exists Y : _, (cardinal U Y n /\ Included U Y A) /\ Im U V Y f = X).