Section tarski_s_euclid_remove_degenerated_cases.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma tarski_s_euclid_remove_degenerated_cases :
(forall A B C D T,
A <> B ->
A <> C ->
A <> D ->
A <> T ->
B <> C ->
B <> D ->
B <> T ->
C <> D ->
C <> T ->
D <> T ->
~ Col A B C ->
Bet A D T ->
Bet B D C ->
~ Col B C T ->
exists x y : Tpoint, Bet A B x /\ Bet A C y /\ Bet x T y) ->
forall A B C D T,
Bet A D T ->
Bet B D C ->
A <> D -> exists x y : Tpoint, Bet A B x /\ Bet A C y /\ Bet x T y.