
theorem
  for K be associative non empty doubleLoopStr for V,W be non empty
ModuleStr over K for a,b be Element of K for f be Form of V,W holds (a*b)*f = a
  *(b*f)
proof
  let K be associative non empty doubleLoopStr, V,W be non empty ModuleStr
  over K, r,s be Element of K, f be Form of V,W;
  now
    let v be Vector of V, w be Vector of W;
    thus ((r*s)*f).(v,w) = (r*s) * f.(v,w) by Def3
      .= r*(s*f.(v,w)) by GROUP_1:def 3
      .= r*(s*f).(v,w) by Def3
      .= (r*(s*f)).(v,w) by Def3;
  end;
  hence thesis;
end;
