Ltac lg_instance l A B :=
assert(tempo_sg:= ex_points_lg l);
match goal with
|H: Q_Cong l |-  _ => assert(tempo_H:=H); apply tempo_sg in tempo_H; elim tempo_H; intros A ; let tempoHP := fresh "tempo_HP" in intro tempoHP; clear tempo_H; elim tempoHP; intro B; intro; clear tempoHP
end;
clear tempo_sg.
Section Length_2.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma is_len_cong : forall A B C D l, Len A B l -> Len C D l -> Cong A B C D.
Lemma is_len_cong_is_len : forall A B C D l, Len A B l -> Cong A B C D -> Len C D l.
Lemma not_cong_is_len : forall A B C D l , ~(Cong A B C D) -> Len A B l -> ~(l C D).
Lemma not_cong_is_len1 : forall A B C D l , ~Cong A B C D -> Len A B l -> ~ Len C D l.
Lemma lg_null_instance : forall l A, Q_Cong_Null l -> l A A.
Lemma lg_null_trivial : forall l A, Q_Cong l -> l A A -> Q_Cong_Null l.
Lemma lg_null_dec : forall l, Q_Cong l -> Q_Cong_Null l \/ ~ Q_Cong_Null l.
Lemma ex_point_lg : forall l A, Q_Cong l -> exists B, l A B.
Lemma ex_point_lg_out : forall l A P, A <> P -> Q_Cong l -> ~ Q_Cong_Null l -> exists B, l A B /\ Out A B P.
Lemma ex_point_lg_bet : forall l A M, Q_Cong l -> exists B : Tpoint, l M B /\ Bet A M B.
End Length_2.