
theorem LM230:
  for x be Element of BOOLEAN*,
  K be Nat
  st len x <> 0 & len x <= K
  holds
  ExAbsval(x) =Absval(ExtBit(x,K))
  proof
    let x be Element of BOOLEAN*,
    K be Nat;
    assume AS: len x <> 0 & len x <= K;
    then
    reconsider n= len x as non zero Nat;
    reconsider y = x as Tuple of n, BOOLEAN by CARD_1:def 7;
    ExtBit(x,K) =y ^ ( 0* (K -' len x) ) by AS,Def20;
    then
    Absval(ExtBit(x,K)) = Absval(y) by LM080
    .= ExAbsval(x) by Def100;
    hence thesis;
  end;
