
theorem Thm20:
  for A,B,C be Point of TOP-REAL 2 st
  A,B,C is_a_triangle holds
  angle(A,B,C) = 2*PI - angle(C,B,A) &
  angle(B,C,A) = 2*PI - angle(A,C,B) &
  angle(C,A,B) = 2*PI - angle(B,A,C) &
  angle(B,A,C) = 2*PI - angle(C,A,B) &
  angle(A,C,B) = 2*PI - angle(B,C,A) &
  angle(C,B,A) = 2*PI - angle(A,B,C)
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume A,B,C is_a_triangle; then
    B,C,A is_a_triangle & C,A,B is_a_triangle &B,A,C is_a_triangle &
    A,C,B is_a_triangle & C,B,A is_a_triangle by MENELAUS:15;
    hence thesis by Lm9;
  end;
