reserve i,j,k,n for Nat;
reserve x,y,z for Tuple of n, BOOLEAN;

theorem Th11:
  i is_expressible_by n implies ADD_MOD(i, NEG_MOD(i,n), n) = 0
proof
  assume i is_expressible_by n;
  then i + NEG_N(i,n) = i + (2 to_power(n) - i) by Def5
    .= 0 + 2 to_power(n);
  hence ADD_MOD(i, NEG_MOD(i,n), n) = 2 to_power(n) mod 2 to_power(n) by
NAT_D:23
    .= 0 by NAT_D:25;
end;
