theorem Th22:
  A,B,C is_a_triangle implies sin angle(A,B,C) <> 0
  proof
    assume
A1: A,B,C is_a_triangle;
    assume
A2: sin angle(A,B,C) = 0;
    the_area_of_polygon3(C,B,A)
        = |.C-B.| * |.A-B.| * sin angle (A,B,C) /2 by EUCLID_6:5
       .= 0 by A2;
    then not C,B,A is_a_triangle by MENELAUS:9;
    hence thesis by A1,MENELAUS:15;
  end;
