Lemma proposition_47B : forall A B C D E F G, Triangle A B C -> Per B A C -> SQ A B F G -> TS G B A C -> SQ B C E D -> TS D C B A -> exists X Y, PG B X Y D /\ BetS B X C /\ PG X C E Y /\ BetS D Y E /\ BetS Y X A /\ Per D Y A /\ EF A B F G B X Y D.