
theorem lemcontr2:
for r,s being Complex holds (r * s) |^ 3 = (r |^ 3) * (s |^ 3)
proof
let r,s be Complex;
thus (r * s) |^ 3
   = (r * s) |^ (2+1)
  .= (r * s) |^ (1+1) * (r * s)  by NEWTON:6
  .= ((r * s)|^ 1 * (r * s)) * (r * s) by NEWTON:6
  .= ((r|^1 * r) * r) * ((s * s) * s)
  .= (r |^(1+1) * r) * ((s * s) * s) by NEWTON:6
  .= r |^(2+1) * ((s|^1 * s) * s) by NEWTON:6
  .= r |^(2+1) * (s|^(1+1) * s) by NEWTON:6
  .= (r |^ 3) * (s |^ 3) by NEWTON:6;
end;
