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 Th17:
  for x,y being Tuple of m, BOOLEAN holds x - y = x + Neg2(y)
proof
  let x,y be Tuple of m, BOOLEAN;
 for i st i in Seg m holds (x - y)/.i
  = (x/.i) 'xor' ((Neg2(y))/.i) 'xor' ((carry(x,Neg2(y)))/.i) by Def6;
  hence thesis by BINARITH:def 5;
end;
