for X, Y being non empty TopSpace
for X1, X2 being non empty SubSpace of X
for f1 being Function of X1,Y
for f2 being Function of X2,Y st ( X1 misses X2 or f1 | (X1 meet X2) = f2 | (X1 meet X2) ) holds
( ( for A being Subset of X1 holds (f1 union f2) .: A = f1 .: A ) & ( for A being Subset of X2 holds (f1 union f2) .: A = f2 .: A ) )