theorem Th24:
  A,C,B is_a_triangle & angle(A,C,B) < PI implies
  angle(B,A,C) + angle(C,B,A) = PI - angle(A,C,B)
  proof
    assume A,C,B is_a_triangle & angle(A,C,B) < PI;
    then angle(A,C,B) = PI - (angle(C,B,A) + angle(B,A,C)) by Th23;
    hence thesis;
  end;
