theorem Thflat05: :: POSET_2:7

for P, Q being non empty flat Poset
for K being non empty Chain of P
for f being Function of P,Q ex a being Element of P st
( ( K = {a} & f .: K = {(f . a)} ) or ( K = {(Bottom P),a} & f .: K = {(f . (Bottom P)),(f . a)} ) )