
theorem
  for n be Nat holds Nat2BL. (2|^n) = (0*n) ^ <*1*>
  proof
    let n be Nat;
    X1: 2|^n = 2 to_power n;
    X3: LenBSeq (2|^n) = [\ log(2,(2|^n)) /] +1 by EXL2
    .= [\ n /] +1 by X1,POWER:def 3
    .= n+1;
    2|^n is Element of NAT by ORDINAL1:def 12; then
    Nat2BL.(2|^n) = (n+1) -BinarySequence (2|^n) by X3,BINARI_6:def 2
    .= (0*n) ^<*1*> by BINARI_3:28,X1;
    hence thesis;
  end;
