Description: A set isweakly dominated by a "larger" set if the "larger" set can be
mapped onto the "smaller" set or the smaller set is empty, or
equivalently, if the smaller set can be placed into bijection with some
partition of the larger set. Dominance ( df-dom ) implies weak
dominance (over ZF). The principle asserting the converse is known as
the partition principle and is independent of ZF. Theorem fodom proves
that the axiom of choice implies the partition principle (over ZF). It
is not known whether the partition principle is equivalent to the axiom
of choice (over ZF), although it is know to imply dependent choice.
(Contributed by Stefan O'Rear, 11-Feb-2015)