reserve a, a9, a1, a2, a3, b, b9, c, c9, d, d9, h, p, q, x, x1, x2, x3, u, v,
  y, z for Real;

theorem Th14:
  (y+h) |^ 3 = y |^ 3+((3*h)*y^2+(3*h^2)*y)+h |^ 3
proof
  (y+h) |^ 3 = (y+h) |^ (2+1);
  then
A1: (y+h) |^ 3 = ((y+h) |^ (1+1))*(y+h) by NEWTON:6
    .= ((y+h) |^ 1*(y+h))*(y+h) by NEWTON:6
    .= ((y+h) |^ 1)*(y+h)^2
    .= ((y+h) to_power 1)*(y^2+2*y*h+h^2) by POWER:41
    .= (y+h)*(y^2+2*y*h+h^2) by POWER:25
    .= y*y^2+((3*h)*y^2+((2+1)*h^2)*y)+h*h^2;
  y |^ 3 = y |^ (2+1) .= (y |^ (1+1))*y by NEWTON:6
    .= (((y |^ 1)*y))*y by NEWTON:6
    .= (y |^ 1)*y^2;
  then
A2: y |^ 3 = (y to_power 1)*y^2by POWER:41;
  h |^ 3 = h |^ (2+1) .= (h |^ (1+1))*h by NEWTON:6
    .= (((h |^ 1)*h))*h by NEWTON:6
    .= (h |^ 1)*h^2
    .= (h to_power 1)*h^2 by POWER:41
    .= h*h^2 by POWER:25;
  hence thesis by A1,A2,POWER:25;
end;
