reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  a > b & a + b >= 2|^(n+1) implies a > 2|^n
  proof
    assume
    A1: a > b & a + b >= 2|^(n+1); then
    a + a > a + b by XREAL_1:6; then
    2*a > 2|^(n+1) by A1,XXREAL_0:2; then
    2*a > 2*2|^n by NEWTON:6;
    hence thesis by XREAL_1:66;
  end;
