(* on_foot *)

(* Specifications: *)
Lemma test_py_on_foot_1  : forall I A B C X Y,
on_foot I A B C -> Py X Y I = Py X Y I.
Lemma test_py_on_foot_2  : forall I A B C X Y,
on_foot I A B C -> Py I Y X = Py X Y I.
Lemma test_py_on_foot_3  : forall I A B C X Y,
on_foot I A B C -> Py X I Y = Py X I Y.
Lemma test_py_on_foot_4  : forall I A B C X,
on_foot I A B C -> Py X I X = Py X I X.
Lemma test_py_on_foot_5 : forall A B C E,
on_foot E B A C ->
Py B E B + Py E A C = Py B E B + Py E A C.
Lemma test_area_on_foot_1  : forall I X Y Z A B,
on_foot I X Y Z -> S A B I = (Py X Y Z * S A B Z + Py X Z Y * S A B Y) / (Py Y Z Y).
Lemma test_area_on_foot_2  : forall I X Y Z A B,
on_foot I X Y Z -> S I A B = (Py X Y Z * S A B Z + Py X Z Y * S A B Y) / (Py Y Z Y).