End T1_3.
Hint Resolve cong_3_sym : cong.
Hint Resolve cong_3_swap cong_3_swap_2 cong3_transitivity : cong3.
Hint Unfold Cong_3 : cong3.
Section T1_4.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma eq_dec_points : forall A B : Tpoint, A=B \/ ~ A=B.
Lemma l2_11 : forall A B C A' B' C',
Bet A B C -> Bet A' B' C' -> Cong A B A' B' -> Cong B C B' C' -> Cong A C A' C'.
Lemma bet_cong3 : forall A B C A' B',  Bet A B C -> Cong A B A' B' -> exists C', Cong_3 A B C A' B' C'.
Lemma construction_uniqueness : forall Q A B C X Y,
Q <> A -> Bet Q A X -> Cong A X B C -> Bet Q A Y -> Cong A Y B C -> X=Y.
Lemma Cong_cases :
forall A B C D,
Cong A B C D \/ Cong A B D C \/ Cong B A C D \/ Cong B A D C \/
Cong C D A B \/ Cong C D B A \/ Cong D C A B \/ Cong D C B A ->
Cong A B C D.
Lemma Cong_perm :
forall A B C D,
Cong A B C D ->
Cong A B C D /\ Cong A B D C /\ Cong B A C D /\ Cong B A D C /\
Cong C D A B /\ Cong C D B A /\ Cong D C A B /\ Cong D C B A.