reserve i,n for Nat;
reserve m for non zero Nat;
reserve p,q for Tuple of n, BOOLEAN;
reserve d,d1,d2 for Element of BOOLEAN;

theorem Th14:
  for z being Tuple of m, BOOLEAN for d being Element of BOOLEAN holds
  Neg2(z^<*d*>) = Neg2(z)^<*'not' d 'xor' add_ovfl('not' z,Bin1(m))*>
proof
  let z be Tuple of m, BOOLEAN;
  let d;
  thus Neg2(z^<*d*>) = 'not' z^<*'not' d*> + Bin1(m+1) by Th9
    .= 'not' z^<*'not' d*> + Bin1(m)^<*FALSE*> by Th7
    .= ('not' z + Bin1(m))^<*'not' d 'xor' FALSE 'xor' add_ovfl('not'
  z,Bin1(m))*> by BINARITH:19
    .= Neg2(z)^<*'not' d 'xor' add_ovfl('not' z,Bin1(m))*>;
end;
