Section Tarski_to_intuitionistic_Tarski.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition BetH A B C : Prop := Bet A B C /\ A <> B /\ B <> C.
Definition T A B C : Prop := ~ (A<>B /\ B<>C /\ ~ BetH A B C).
Definition ColB A B C := ~ (~ T C A B /\ ~ T A C B /\ ~ T A B C).

Lemma between_inner_transitivity_B : forall A B C D : Tpoint, BetH A B D -> BetH B C D -> BetH A B C.