
theorem Th17:
  for K be associative non empty multMagma for V be non empty
ModuleStr over K for r,s be Element of K for f be Functional of V holds (r*s)*f
  = r*(s*f)
proof
  let K be associative non empty multMagma;
  let V be non empty ModuleStr over K;
  let r,s be Element of K;
  let f be Functional of V;
  now
    let x be Element of V;
    thus ((r*s)*f).x = (r*s)*f.x by Def6
      .= r*(s*f.x) by GROUP_1:def 3
      .= r*(s*f).x by Def6
      .= (r*(s*f)).x by Def6;
  end;
  hence thesis by FUNCT_2:63;
end;
