End T1_1.
Hint Resolve cong_commutativity cong_3421 cong_4312 cong_4321 cong_trivial_identity
cong_left_commutativity cong_right_commutativity
cong_transitivity cong_symmetry cong_reflexivity : cong.
Ltac Cong := auto 4 with cong.
Ltac eCong := eauto with cong.
Section T1_2.
Context `{Tn:Tarski_neutral_dimensionless}.
(* We pre-compute some trivial lemmas to have more efficient automatic proofs. *)

(* Specifications: *)
Lemma not_cong_2134 : forall A B C D, ~ Cong A B C D -> ~ Cong B A C D.
Lemma not_cong_1243 : forall A B C D, ~ Cong A B C D -> ~ Cong A B D C.
Lemma not_cong_2143 : forall A B C D, ~ Cong A B C D -> ~ Cong B A D C.
Lemma not_cong_3412 : forall A B C D, ~ Cong A B C D -> ~ Cong C D A B.
Lemma not_cong_4312 : forall A B C D, ~ Cong A B C D -> ~ Cong D C A B.
Lemma not_cong_3421 : forall A B C D, ~ Cong A B C D -> ~ Cong C D B A.
Lemma not_cong_4321 : forall A B C D, ~ Cong A B C D -> ~ Cong D C B A.
End T1_2.