
theorem
  for f being complex-valued Function, g being Function st dom f = dom g
  & for c being object st c in dom f holds g.c = -(f.c) holds g = -f
proof
  let f be complex-valued Function, g be Function;
  assume that
A1: dom f = dom g and
A2: for c being object st c in dom f holds g.c = -(f.c);
  thus dom -f = dom g by A1,Def5;
  let c be object;
  assume
A3: c in dom g;
  thus (-f).c = -f.c by Th8
    .= g.c by A1,A2,A3;
end;
