(* inter_ll *)

(* Specifications: *)
Lemma  test_inter_ll_1 : forall I A B C D X Y,
inter_ll I A B C D -> Py I X Y = Py Y X I.
Lemma  test_inter_ll_2 : forall I A B C D X Y,
inter_ll I A B C D -> Py Y X I = Py Y X I.
Lemma  test_inter_ll_3 : forall I A B C D X Y,
inter_ll I A B C D -> Py Y I X = Py Y I X.
Lemma  test_inter_ll_4 : forall I A B C D X,
inter_ll I A B C D -> Py X I X = Py X I X.
Lemma test_area_inter_ll_1 : forall I A B C D X Y,
inter_ll I A B C D -> S X Y I = 1 / S4 A C B D * (S A C D * S X Y B + S B D C * S X Y A) .
Lemma test_area_inter_ll_2  : forall I A B C D X Y,
inter_ll I A B C D -> S I X Y = 1 / S4 A C B D * (S A C D * S X Y B + S B D C * S X Y A) .
Lemma test_area_inter_ll_3  : forall I A B C D X Y,
inter_ll I A B C D -> S Y I X = 1 / S4 A C B D * (S A C D * S X Y B + S B D C * S X Y A) .
Lemma test_area_on_parallel_1  : forall I B C D X Y,
on_parallel I B C D -> S X Y I = S X Y B + B ** I / C ** D * S4 X C Y D.
Lemma test_area_on_parallel_2  : forall I B C D X Y,
on_parallel I B C D -> S Y I X = S X Y B + B ** I / C ** D * S4 X C Y D.
Lemma test_area_on_parallel_3  : forall I B C D X Y,
on_parallel I B C D -> S I X Y = S X Y B + B ** I / C ** D * S4 X C Y D.
Lemma test_area_on_parallel_d_1  : forall I B C D X Y r,
on_parallel_d I B C D r -> S I X Y = S X Y B + r * S4 X C Y D.
Lemma test_area_on_parallel_d_2  : forall I B C D X Y r,
on_parallel_d I B C D r -> S X Y I = S X Y B + r * S4 X C Y D.
Lemma test_area_on_parallel_d_3  : forall I B C D X Y r,
on_parallel_d I B C D r -> S Y I X = S X Y B + r * S4 X C Y D.
Lemma test_area_on_inter_line_parallel_1 : forall I A B C D E X Y,
on_inter_line_parallel I A B C D E -> False ->
S X Y I = (S4 D B E A * S X Y C - S4 D C E A * S X Y B) / S4 D B E C .
Lemma test_area_on_inter_parallel_parallel_1 : forall I A B C D E F X Y,
on_inter_parallel_parallel I A B C D E F ->
False ->
S X Y I = S4 B D C A / S4 B E C F * S4 X E Y F + S X Y D.