(** * Proposition 17 In any triangle two angles taken together in any manner are less than two right angles. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container17"></div> # **)
(** Here, the fact that the two angles are less than two right angles is described with the SAMS predicate, which means that they have a "sum at most straight", and the fact that their sum is not a straight line. *)

Lemma prop_17 : forall A B C P Q R, ~ Col A B C -> SumA A B C B C A P Q R ->
SAMS A B C B C A /\ ~ Bet P Q R.