Ltac anga_instance1 a A B C :=
assert(tempo_anga:= anga_const a A B);
match goal with
|H: Q_CongA_Acute a |-  _ => assert(tempo_H:= H); apply tempo_anga in tempo_H; ex_elim tempo_H C
end;
clear tempo_anga.
Section Angles_5.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma null_anga_null_anga' : forall a, Q_CongA_Null_Acute a <-> is_null_anga' a.
Lemma is_null_anga_out : forall a A B C, Q_CongA_Acute a -> a A B C -> Q_CongA_Null_Acute a -> Out B A C.
Lemma acute_not_bet : forall A B C, Acute A B C -> ~Bet A B C.
Lemma anga_acute : forall a A B C , Q_CongA_Acute a -> a A B C -> Acute A B C.
Lemma not_null_not_col : forall a A B C, Q_CongA_Acute a -> ~ Q_CongA_Null_Acute a -> a A B C -> ~Col A B C.
Lemma ang_cong_ang : forall a A B C A' B' C', Q_CongA a -> a A B C -> CongA A B C A' B' C' -> a A' B' C'.
Lemma is_null_ang_out : forall a A B C, Q_CongA a -> a A B C -> Q_CongA_Null a -> Out B A C.
Lemma out_null_ang : forall a A B C, Q_CongA a -> a A B C -> Out B A C -> Q_CongA_Null a.
Lemma bet_flat_ang : forall a A B C, Q_CongA a -> a A B C -> Bet A B C -> Ang_Flat a.
Lemma out_null_anga : forall a A B C, Q_CongA_Acute a -> a A B C -> Out B A C -> Q_CongA_Null_Acute a.
Lemma anga_not_flat : forall a, Q_CongA_Acute a -> Q_CongA_nFlat a.
Lemma anga_const_o : forall a A B P, ~Col A B P -> ~ Q_CongA_Null_Acute a -> Q_CongA_Acute a -> exists C, a A B C /\ OS A B C P.
Lemma anga_conga_anga : forall a A B C A' B' C' , Q_CongA_Acute a -> a A B C -> CongA A B C A' B' C' -> a A' B' C'.
Lemma anga_out_anga : forall a A B C A' C', Q_CongA_Acute a -> a A B C -> Out B A A' -> Out B C C' -> a A' B C'.
Lemma out_out_anga : forall a A B C A' B' C', Q_CongA_Acute a -> Out B A C -> Out B' A' C' -> a A B C -> a A' B' C'.
Lemma is_null_all : forall a A B, A <> B -> Q_CongA_Null_Acute a -> a A B A.
Lemma anga_col_out : forall a A B C, Q_CongA_Acute a -> a A B C -> Col A B C -> Out B A C.
Lemma ang_not_lg_null : forall a la lc A B C, Q_Cong la -> Q_Cong lc -> Q_CongA a ->
la A B -> lc C B -> a A B C -> ~ Q_Cong_Null la /\ ~ Q_Cong_Null lc.
Lemma anga_not_lg_null : forall a la lc A B C, Q_Cong la -> Q_Cong lc ->
Q_CongA_Acute a -> la A B -> lc C B -> a A B C -> ~ Q_Cong_Null la /\ ~ Q_Cong_Null lc.
Lemma anga_col_null : forall a A B C, Q_CongA_Acute a -> a A B C -> Col A B C -> Out B A C /\ Q_CongA_Null_Acute a.
Lemma eqA_preserves_ang: forall a b, Q_CongA a -> EqA a b -> Q_CongA b.
Lemma eqA_preserves_anga : forall a b, Q_CongA_Acute a -> Q_CongA b -> EqA a b -> Q_CongA_Acute b.
End Angles_5.