theorem :: RFUNCT_2:37

for X, Y being set
for h1, h2 being PartFunc of REAL,REAL holds
( ( h1 | X is increasing & h2 | Y is increasing implies (h1 + h2) | (X /\ Y) is increasing ) & ( h1 | X is decreasing & h2 | Y is decreasing implies (h1 + h2) | (X /\ Y) is decreasing ) & ( h1 | X is non-decreasing & h2 | Y is non-decreasing implies (h1 + h2) | (X /\ Y) is non-decreasing ) & ( h1 | X is non-increasing & h2 | Y is non-increasing implies (h1 + h2) | (X /\ Y) is non-increasing ) )