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. *)

Lemma not_cong_3412 : forall A B C D, ~ Cong A B C D -> ~ Cong C D A B.