theorem Th32: :: RFUNCT_2:32

for Y being set
for r being Real
for h being PartFunc of REAL,REAL holds
( ( h | Y is increasing & 0 < r implies (r (#) h) | Y is increasing ) & ( r = 0 implies (r (#) h) | Y is constant ) & ( h | Y is increasing & r < 0 implies (r (#) h) | Y is decreasing ) )