Require Export GeoCoq.Tarski_dev.Annexes.saccheri.
Section Defect.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma defect_distincts : forall A B C D E F,
Defect A B C D E F ->
A <> B /\ B <> C /\ A <> C /\ D <> E /\ E <> F.
Lemma ex_defect : forall A B C,
A <> B -> B <> C -> A <> C -> exists D E F, Defect A B C D E F.
Lemma conga_defect__defect : forall A B C D E F D' E' F',
Defect A B C D E F -> CongA D E F D' E' F' ->
Defect A B C D' E' F'.
Lemma defect2__conga : forall A B C D E F D' E' F',
Defect A B C D E F -> Defect A B C D' E' F' ->
CongA D E F D' E' F'.
Lemma defect_perm_231 : forall A B C D E F,
Defect A B C D E F -> Defect B C A D E F.
Lemma defect_perm_312 : forall A B C D E F,
Defect A B C D E F -> Defect C A B D E F.
Lemma defect_perm_321 : forall A B C D E F,
Defect A B C D E F -> Defect C B A D E F.
Lemma defect_perm_213 : forall A B C D E F,
Defect A B C D E F -> Defect B A C D E F.
Lemma defect_perm_132 : forall A B C D E F,
Defect A B C D E F -> Defect A C B D E F.
Lemma conga3_defect__defect : forall A B C D E F A' B' C',
Defect A B C D E F ->
CongA A B C A' B' C' -> CongA B C A B' C' A' -> CongA C A B C' A' B' ->
Defect A' B' C' D E F.
Lemma col_defect__out : forall A B C D E F,
Col A B C -> Defect A B C D E F -> Out E D F.
Lemma rah_defect__out :
hypothesis_of_right_saccheri_quadrilaterals ->
forall A B C D E F, Defect A B C D E F -> Out E D F.
Lemma defect_ncol_out__rah : forall A B C D E F,
~ Col A B C -> Defect A B C D E F -> Out E D F ->
hypothesis_of_right_saccheri_quadrilaterals.