
theorem Th6:
  for f being complex-valued Function, r being Complex for c
  being object holds (r(#)f).c = r * f.c
proof
  let f be complex-valued Function, r be Complex;
  let c be object;
A1: dom f = dom (r(#)f) by Def5;
  per cases;
  suppose
    c in dom f;
    hence thesis by A1,Def5;
  end;
  suppose
A2: not c in dom f;
    hence (r(#)f).c = r*0 by A1,FUNCT_1:def 2
      .= r * f.c by A2,FUNCT_1:def 2;
  end;
end;
