
theorem
  for A,B,C be Point of TOP-REAL 2 st
  A,B,C is_a_triangle & angle(C,A,B)<PI holds
  angle (C,B,A) + angle (B,A,C) + angle (A,C,B) = 5 * PI &
  angle (C,A,B) + angle (A,B,C) + angle (B,C,A) = PI
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume that
A1: A,B,C is_a_triangle and
A2: angle(C,A,B)<PI;
    B,A,C is_a_triangle by A1,MENELAUS:15;
    hence thesis by A2,Lm11;
  end;
