End T12_2.
Section T12_2'.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma l12_6 : forall A B C D,
Par_strict A B C D -> OS A B C D.
Lemma pars__os3412 : forall A B C D,
Par_strict A B C D -> OS C D A B.
Lemma perp_dec : forall A B C D, Perp A B C D \/ ~ Perp A B C D.
Lemma col_cop2_perp2__col : forall X1 X2 Y1 Y2 A B,
Perp X1 X2 A B -> Perp Y1 Y2 A B -> Col X1 Y1 Y2 ->
Coplanar A B X2 Y1 -> Coplanar A B X2 Y2 -> Col X2 Y1 Y2.
Lemma col_perp2_ncol__col : forall X1 X2 Y1 Y2 A B,
Perp X1 X2 A B -> Perp Y1 Y2 A B ->
Col X1 Y1 Y2 -> ~ Col X1 A B ->
Col X2 Y1 Y2.
Lemma l12_9 : forall A1 A2 B1 B2 C1 C2,
Coplanar C1 C2 A1 B1 -> Coplanar C1 C2 A1 B2 ->
Coplanar C1 C2 A2 B1 -> Coplanar C1 C2 A2 B2 ->
Perp A1 A2 C1 C2 -> Perp B1 B2 C1 C2 ->
Par A1 A2 B1 B2.