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(* Specifications: *)
Lemma plgf_trivial : forall A B, A <> B -> Parallelogram_flat A B B A.
Lemma plgf3_mid : forall A B C, Parallelogram_flat A B A C -> Midpoint A B C.
Lemma cong3_id : forall A B C D, A <> B -> Col A B C -> Col A B D -> Cong A B C D -> Cong A D B C -> Cong A C B D
-> A = D /\ B = C \/ A = C /\ B = D.
Lemma col_cong_mid1 : forall A B C D, A <> D -> Col A B C -> Col A B D -> Cong A B C D -> Cong A C B D
-> exists M, Midpoint M A D /\ Midpoint M B C.
Lemma col_cong_mid2 : forall A B C D, A <> C -> Col A B C -> Col A B D -> Cong A B C D -> Cong A D B C
-> exists M, Midpoint M A C /\ Midpoint M B D.