theorem
  for A,B be non empty set
  for A1,A2 be non empty Subset of A
  for f1 be Function of A1,B, f2 be Function of A2,B
  st f1|(A1 /\ A2) = f2|(A1 /\ A2) holds
  (f1 union f2)|A1 = f1 & (f1 union f2)|A2 = f2 by Def1;
