Definition parallelogram (A B C D : Point) : Prop :=
  parallel A B C D /\ parallel B C A D /\ ~ Col A B C.

(* Specifications: *)
Theorem diago_par_intersect : forall A B C D : Point, parallelogram A B C D -> ~ parallel A C B D.
Theorem para_not_col_1 : forall A B C D : Point, parallelogram A B C D -> ~ Col A B D.
Theorem para_not_col_2 : forall A B C D : Point, parallelogram A B C D -> ~ Col B C D.
Theorem para_not_col_3 : forall A B C D : Point, parallelogram A B C D -> ~ Col A C D.
Theorem para_1 : forall A B C D : Point, parallelogram A B C D -> parallelogram A D C B.
Theorem para_2 : forall A B C D : Point, parallelogram A B C D -> parallelogram B A D C.
Theorem para_3 : forall A B C D : Point, parallelogram A B C D -> parallelogram D C B A.
Theorem para_4 : forall A B C D : Point, parallelogram A B C D -> parallelogram C B A D.
Theorem not_para_eq_1 : forall A B C, ~ parallelogram A A B C.
Theorem not_para_eq_2 : forall A B C, ~ parallelogram A B C C.
Theorem not_para_eq_3 : forall A B C, ~ parallelogram A B C A.
Theorem not_para_eq_4 : forall A B C, ~ parallelogram A B B C.
Theorem not_para_eq_5 : forall A B C, ~ parallelogram A B A C.
Theorem not_para_eq_6 : forall A B C, ~ parallelogram A B C B.
Theorem para_not_eq_1 : forall A B C D, parallelogram A B C D -> A<>B.
Theorem para_not_eq_2 : forall A B C D, parallelogram A B C D -> A<>C.
Theorem para_not_eq_3 : forall A B C D, parallelogram A B C D -> A<>D.
Theorem para_not_eq_4 : forall A B C D, parallelogram A B C D -> B<>C.
Theorem para_not_eq_5 : forall A B C D, parallelogram A B C D -> B<>D.
Theorem para_not_eq_6 : forall A B C D, parallelogram A B C D -> C<>D.
Theorem col_par_par : forall A B C D D', ~C=D -> parallel A B C D -> Col C D D' -> parallel A B C D'.