
theorem LMC31B:
  for m,n be Nat holds m <= m to_power (n+1)
  proof
    let m,n be Nat;
    per cases by NAT_1:14;
    suppose m = 0;
      hence thesis;
    end;
    suppose
A1:   1 <= m;
      1 <= n+1 by NAT_1:11; then
      m to_power 1 <= m to_power (n+1) by A1,PRE_FF:8;
      hence thesis by NEWTON:5;
    end;
  end;
