(* We use the square to get rid of sign issues *)

(* Specifications: *)
Axiom on_foot_area : forall A B C F,
on_foot F A B C ->
2 * 2 * S A B C * S A B C = A**F * A**F * B**C * B**C.
Lemma on_foot_area_paper : forall A B C F,
perp F A B C -> Col F B C ->
2 * 2 * S A B C * S A B C = A**F * A**F * B**C * B**C.
Lemma pyth_simpl_1 : forall A B, Py A A B = 0.
Lemma pyth_simpl_2 : forall A B, Py A B B = 0.
Hint Rewrite pyth_simpl_1  pyth_simpl_2 : seg_simplifications.