theorem Th42: :: STIRL2_1:42

for k, n being Nat holds card { f where f is Function of (Segm (n + 1)),(Segm (k + 1)) : ( f is onto & f is "increasing & f " {(f . n)} = {n} ) } = card { f where f is Function of (Segm n),(Segm k) : ( f is onto & f is "increasing ) }