
theorem THY3:
  dist(|[1,0]|,|[0,1]|) = sqrt 2
  proof
    dist(|[1,0]|,|[0,1]|) = sqrt ((1-0)^2+(0 - 1)^2) by THYQ
                         .= sqrt (1^2+(1)^2) by SQUARE_1:3
                         .= sqrt (1 * 1 + 1^2) by SQUARE_1:def 1
                         .= sqrt (1 * 1 + 1 * 1) by SQUARE_1:def 1
                         .= sqrt 2;
    hence thesis;
  end;
