
theorem Thm19:
  for A,B,C being Point of TOP-REAL 2 st A,B,C is_a_triangle holds
  angle(A,B,C) is non zero & angle(B,C,A) is non zero &
  angle(C,A,B) is non zero & angle(A,C,B) is non zero &
  angle(C,B,A) is non zero & angle(B,A,C) is non zero
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume
A1: 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 A1,Lm7;
  end;
