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(* Specifications: *)
Lemma plg_trivial : forall A B, A <> B -> Parallelogram A B B A.
Lemma plg_trivial1 : forall A B, A <> B -> Parallelogram A A B B.
Lemma col_not_plgs : forall A B C D, Col A B C -> ~Parallelogram_strict A B C D.
Lemma plg_col_plgf : forall A B C D, Col A B C -> Parallelogram A B C D -> Parallelogram_flat A B C D.
Lemma plg_bet1 : forall A B C D, Parallelogram A B C D -> Bet A C B -> Bet D A C.
Lemma plgf_trivial1 : forall A B, A <> B -> Parallelogram_flat A B B A.
Lemma plgf_trivial2 : forall A B, A <> B -> Parallelogram_flat A A B B.
Lemma plgf_not_point : forall A B, Parallelogram_flat A A B B -> A <> B.
Lemma plgf_trivial_neq : forall A C D, Parallelogram_flat A A C D -> C = D /\ A <> C.
Lemma plgf_trivial_trans : forall A B C, Parallelogram_flat A A B B -> Parallelogram_flat B B C C
-> Parallelogram_flat A A C C \/ A = C.