
theorem
  for f1,f2 being complex-valued Function, f being Function st dom f =
  dom (f1-f2) & for c being object st c in dom f holds f.c = f1.c - f2.c
   holds f = f1-f2
proof
  let f1,f2 be complex-valued Function, f be Function such that
A1: dom f = dom (f1-f2) and
A2: for c being object st c in dom f holds f.c = f1.c - f2.c;
  thus dom f = dom (f1-f2) by A1;
  let c be object;
  assume
A3: c in dom f;
  hence f.c = f1.c - f2.c by A2
    .= f1.c+(-f2).c by Th8
    .= (f1-f2).c by A1,A3,Def1;
end;
