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

theorem Th3:
  |.F-E.|^2 = |.A-E.|^2 + |.A-F.|^2 - 2 * |.A-E.| * |.A-F.| * cos angle(E,A,F)
  proof
    |.F-E.|^2 = |.E-A.|^2 + |.F-A.|^2 - 2*|.E-A.|*|.F-A.|*cos angle (E,A,F)
            by EUCLID_6:7
         .= |.A-E.|^2 + |.F-A.|^2 - 2*|.E-A.|*|.F-A.|*cos angle (E,A,F)
            by EUCLID_6:43
         .= |.A-E.|^2 + |.A-F.|^2 - 2*|.E-A.|*|.F-A.|*cos angle (E,A,F)
            by EUCLID_6:43
         .= |.A-E.|^2 + |.A-F.|^2 - 2*|.A-E.|*|.F-A.|*cos angle (E,A,F)
            by EUCLID_6:43
         .= |.A-E.|^2 + |.A-F.|^2 - 2*|.A-E.|*|.A-F.|*cos angle (E,A,F)
            by EUCLID_6:43;
    hence thesis;
  end;
