
theorem EXL2:
  for n be Nat st 0 < n holds
  LenBSeq n = [\ log(2,n) /] +1
  proof
    let n be Nat;
    assume 0 < n; then
    consider x be Nat such that
LCX:2 to_power x <= n & n < 2 to_power (x + 1) &
      LenBSeq n = x+1 by BINARI_6:def 1;
    log(2,2 to_power x) = x by POWER:def 3; then
    LT1: x <= log(2,n) by LCX, ASYMPT_2:7;
    log(2,2 to_power (x+1)) = x+1 by POWER:def 3; then
    log(2,n) < x+1 by LCX,POWER:57; then
    log(2,n) - 1 < x+1-1 by XREAL_1:14;
    hence thesis by LCX,LT1,INT_1:def 6;
  end;
