reserve A,B,C,D,E,F,G for Point of TOP-REAL 2;

theorem Th5:
  angle(C,B,A) < PI implies 0 <= the_area_of_polygon3(A,B,C)
  proof
    assume angle(C,B,A) < PI;
    then 2*PI*0 <= angle(C,B,A) < PI+2*PI*0 by Th2;
    then
A1: sin angle(C,B,A) >=0 by SIN_COS6:16;
    the_area_of_polygon3(A,B,C) = |.A-B.| * |.C-B.| * sin angle(C,B,A) /2
    by EUCLID_6:5;
    hence thesis by A1;
  end;
