reserve a,b,c,d,x,j,k,l,m,n for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  2|^(3+m) + 2|^(3+m) < 3|^(3+m)
  proof
    A4: 2|^(2+1) + 2|^(2+1) = 2*2|^(2+1)
    .= 2*(2*2|^2) by NEWTON:6 .= 2*(2*2*2) by NEWTON:81;
    A5: 3|^(2+1) = 3*3|^2 by NEWTON:6 .= 3*3*3 by NEWTON:81;
    A6: 2|^(3+m) = 2|^3 * 2|^m & 3|^(3+m) = 3|^3 * 3|^m by NEWTON:8;
    2|^m <= 3|^m by Lm3a; then
    A7: ((2|^3)+(2|^3))*(2|^m) <= ((2|^3)+(2|^3))*(3|^m) by XREAL_1:64;
    3|^m > 0 by PREPOWER:6; then
    ((2|^3)+(2|^3))*(3|^m) < (3|^3)*(3|^m) by A4,A5,XREAL_1:68;
    hence thesis by XXREAL_0:2,A6,A7;
  end;
