theorem Th1: :: TMAP_1:1

for A, B being non empty set
for A1, A2 being non empty Subset of A st A1 misses A2 holds
for f1 being Function of A1,B
for f2 being Function of A2,B holds
( f1 | (A1 /\ A2) = f2 | (A1 /\ A2) & (f1 union f2) | A1 = f1 & (f1 union f2) | A2 = f2 )