Section Coplanar_perm.
Context `{Tn:Tarski_neutral_dimensionless}.

(* Specifications: *)
Lemma coplanar_perm_1 : forall A B C D,
Coplanar A B C D -> Coplanar A B D C.
Lemma coplanar_perm_2 : forall A B C D,
Coplanar A B C D -> Coplanar A C B D.
Lemma coplanar_perm_3 : forall A B C D,
Coplanar A B C D -> Coplanar A C D B.
Lemma coplanar_perm_4 : forall A B C D,
Coplanar A B C D -> Coplanar A D B C.
Lemma coplanar_perm_5 : forall A B C D,
Coplanar A B C D -> Coplanar A D C B.
Lemma coplanar_perm_6 : forall A B C D,
Coplanar A B C D -> Coplanar B A C D.
Lemma coplanar_perm_7 : forall A B C D,
Coplanar A B C D -> Coplanar B A D C.
Lemma coplanar_perm_8 : forall A B C D,
Coplanar A B C D -> Coplanar B C A D.
Lemma coplanar_perm_9 : forall A B C D,
Coplanar A B C D -> Coplanar B C D A.
Lemma coplanar_perm_10 : forall A B C D,
Coplanar A B C D -> Coplanar B D A C.
Lemma coplanar_perm_11 : forall A B C D,
Coplanar A B C D -> Coplanar B D C A.
Lemma coplanar_perm_12 : forall A B C D,
Coplanar A B C D -> Coplanar C A B D.
Lemma coplanar_perm_13 : forall A B C D,
Coplanar A B C D -> Coplanar C A D B.
Lemma coplanar_perm_14 : forall A B C D,
Coplanar A B C D -> Coplanar C B A D.
Lemma coplanar_perm_15 : forall A B C D,
Coplanar A B C D -> Coplanar C B D A.
Lemma coplanar_perm_16 : forall A B C D,
Coplanar A B C D -> Coplanar C D A B.
Lemma coplanar_perm_17 : forall A B C D,
Coplanar A B C D -> Coplanar C D B A.
Lemma coplanar_perm_18 : forall A B C D,
Coplanar A B C D -> Coplanar D A B C.
Lemma coplanar_perm_19 : forall A B C D,
Coplanar A B C D -> Coplanar D A C B.
Lemma coplanar_perm_20 : forall A B C D,
Coplanar A B C D -> Coplanar D B A C.
Lemma coplanar_perm_21 : forall A B C D,
Coplanar A B C D -> Coplanar D B C A.
Lemma coplanar_perm_22 : forall A B C D,
Coplanar A B C D -> Coplanar D C A B.
Lemma coplanar_perm_23 : forall A B C D,
Coplanar A B C D -> Coplanar D C B A.
Lemma ncoplanar_perm_1 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar A B D C.
Lemma ncoplanar_perm_2 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar A C B D.
Lemma ncoplanar_perm_3 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar A C D B.
Lemma ncoplanar_perm_4 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar A D B C.
Lemma ncoplanar_perm_5 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar A D C B.
Lemma ncoplanar_perm_6 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B A C D.
Lemma ncoplanar_perm_7 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B A D C.
Lemma ncoplanar_perm_8 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B C A D.
Lemma ncoplanar_perm_9 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B C D A.
Lemma ncoplanar_perm_10 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B D A C.
Lemma ncoplanar_perm_11 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar B D C A.
Lemma ncoplanar_perm_12 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C A B D.
Lemma ncoplanar_perm_13 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C A D B.
Lemma ncoplanar_perm_14 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C B A D.
Lemma ncoplanar_perm_15 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C B D A.
Lemma ncoplanar_perm_16 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C D A B.
Lemma ncoplanar_perm_17 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar C D B A.
Lemma ncoplanar_perm_18 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D A B C.
Lemma ncoplanar_perm_19 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D A C B.
Lemma ncoplanar_perm_20 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D B A C.
Lemma ncoplanar_perm_21 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D B C A.
Lemma ncoplanar_perm_22 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D C A B.
Lemma ncoplanar_perm_23 : forall A B C D,
~ Coplanar A B C D -> ~ Coplanar D C B A.
Lemma coplanar_trivial : forall A B C, Coplanar A A B C.
Lemma col__coplanar : forall A B C D,
Col A B C -> Coplanar A B C D.
Lemma ncop__ncol : forall A B C D,
~ Coplanar A B C D -> ~ Col A B C.
Lemma ncop__ncols : forall A B C D,
~ Coplanar A B C D -> ~ Col A B C /\ ~ Col A B D /\ ~ Col A C D /\ ~ Col B C D.
Lemma bet__coplanar : forall A B C D,
Bet A B C -> Coplanar A B C D.
Lemma out__coplanar : forall A B C D,
Out A B C -> Coplanar A B C D.
Lemma midpoint__coplanar : forall A B C D,
Midpoint A B C -> Coplanar A B C D.
Lemma perp__coplanar : forall A B C D,
Perp A B C D -> Coplanar A B C D.
Lemma ts__coplanar : forall A B C D,
TS A B C D -> Coplanar A B C D.
Lemma reflectl__coplanar : forall A B C D,
ReflectL A B C D -> Coplanar A B C D.
Lemma reflect__coplanar : forall A B C D,
Reflect A B C D -> Coplanar A B C D.
Lemma inangle__coplanar : forall A B C D,
InAngle A B C D -> Coplanar A B C D.
Lemma pars__coplanar : forall A B C D,
Par_strict A B C D -> Coplanar A B C D.
Lemma par__coplanar : forall A B C D,
Par A B C D -> Coplanar A B C D.
Lemma plg__coplanar : forall A B C D,
Plg A B C D -> Coplanar A B C D.
Lemma plgs__coplanar : forall A B C D,
Parallelogram_strict A B C D -> Coplanar A B C D.
Lemma plgf__coplanar : forall A B C D,
Parallelogram_flat A B C D -> Coplanar A B C D.
Lemma parallelogram__coplanar : forall A B C D,
Parallelogram A B C D -> Coplanar A B C D.
Lemma rhombus__coplanar : forall A B C D,
Rhombus A B C D -> Coplanar A B C D.
Lemma rectangle__coplanar : forall A B C D,
Rectangle A B C D -> Coplanar A B C D.
Lemma square__coplanar : forall A B C D,
Square A B C D -> Coplanar A B C D.
Lemma lambert__coplanar : forall A B C D,
Lambert A B C D -> Coplanar A B C D.