(** * Proposition 10 To bisect a given finite straight line. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container10"></div> # **)

(* Specifications: *)
Lemma prop_10 : forall A B, exists D, Midpoint D A B.
(** * Proposition 11 To draw a straight line at right angles to a given straight line from a given point on it. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container11"></div> # **)
Lemma prop_11 : forall A B C, A <> B -> Col A B C -> exists F, Perp C F A B.
(** * Proposition 12 To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container12"></div> # **)
Lemma prop_12 : forall A B C, ~ Col A B C -> exists H, Col A B H /\ Perp A B C H.
(** * Proposition 13 If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container13"></div> # **)
Lemma prop_13 : forall A B C D P Q R, A <> B -> B <> C -> B <> D -> Bet C B D ->
P <> Q -> Q <> R -> Per P Q R ->
SumA C B A A B D C B D /\ SumA P Q R P Q R C B D.