Section SPP_tarski.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma strong_parallel_postulate_implies_tarski_s_euclid_aux :
strong_parallel_postulate ->
(forall A B D T,
A <> B ->
A <> D ->
A <> T ->
B <> D ->
B <> T ->
D <> T ->
~ Col A B T ->
Bet A D T ->
exists B', exists B'', exists MB, exists X, Bet A B X /\ Par_strict T X B D /\
BetS B MB T /\ BetS B' MB B'' /\
Cong B MB T MB /\ Cong B' MB B'' MB /\
Col B B' D /\ Bet B'' T X /\
B <> B' /\ B'' <> T).