
theorem Th10:
  for f being complex-valued Function for c being object holds
  f".c = (f.c)"
proof
  let f be complex-valued Function;
  let c be object;
A1: dom (f") = dom f by Def7;
  per cases;
  suppose
    c in dom f;
    hence thesis by A1,Def7;
  end;
  suppose
A2: not c in dom f;
    hence f".c = 0 qua Complex" by A1,FUNCT_1:def 2
      .= (f.c)" by A2,FUNCT_1:def 2;
  end;
end;
