reserve a, b, c, d, x, y, z for Complex;
reserve r for Real;

theorem Th70:
  angle(a,b,c) = angle(a+d,b+d,c+d)
proof
  thus angle(a,b,c) = angle(a-b,0c,c-b) by Th69
    .= angle((a+d)-(b+d),0c,(c+d)-(b+d))
    .= angle(a+d,b+d,c+d) by Th69;
end;
