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

theorem Th14:
  ADD_MOD(ADD_MOD(i,j,n),k,n) = ADD_MOD(i,ADD_MOD(j,k,n),n)
proof
  thus ADD_MOD(ADD_MOD(i,j,n),k,n) = (i+j+k) mod 2 to_power(n) by NAT_D:23
    .= (i+(j+k)) mod 2 to_power(n)
    .= ADD_MOD(i,ADD_MOD(j,k,n),n) by NAT_D:22;
end;
