
theorem LM006:
  for x be Nat holds x < 2 to_power LenBSeq x
  proof
    let x be Nat;
    per cases;
    suppose C1: x=0; then
      LenBSeq x = 1 by Def1;
      hence x < 2 to_power LenBSeq x by POWER:25,C1;
    end;
    suppose x <> 0; then
      consider n be Nat such that
      C2: 2 to_power n <= x & x < 2 to_power (n + 1)
      & LenBSeq x = n+1 by Def1;
      thus x < 2 to_power LenBSeq x by C2;
    end;
  end;
