reserve p1,p2,p3,p4,p5,p6,p,pc for Point of TOP-REAL 2;
reserve a,b,c,r,s for Real;

theorem Th3:
  cos angle(p1,p2,p3) = cos angle(p3,p2,p1)
proof
  per cases;
  suppose
    angle(p1,p2,p3)=0;
    hence thesis by EUCLID_3:36;
  end;
  suppose
    angle(p1,p2,p3)<>0;
    then angle(p3,p2,p1)=2*PI-angle(p1,p2,p3) by EUCLID_3:37;
    then cos angle(p1,p2,p3) = cos(-angle(p3,p2,p1)+2*PI)
      .= cos(-angle(p3,p2,p1)) by SIN_COS:79
      .= cos(angle(p3,p2,p1)) by SIN_COS:31;
    hence thesis;
  end;
end;
