Ltac anga_instance_o a A B P C :=
        assert(tempo_anga:= anga_const_o a A B P);
        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.

(* Specifications: *)
Lemma l13_6 : forall a lc ld l, Lcos lc l a -> Lcos ld l a -> EqL lc ld.
Lemma null_lcos_eql : forall lp l a, Lcos lp l a -> Q_CongA_Null_Acute a -> EqL l lp.
Lemma eql_lcos_null : forall l lp a, Lcos l lp a -> EqL l lp -> Q_CongA_Null_Acute a.
Lemma lcos_lg_not_null: forall l lp a, Lcos l lp a -> ~ Q_Cong_Null l /\ ~ Q_Cong_Null lp.
Lemma perp_acute_out : forall A B C C', Acute A B C -> Perp A B C C' -> Col A B C' -> Out B A C'.
Lemma perp_out__acute : forall A B C C', Perp A B C C' -> Col A B C' -> (Acute A B C <-> Out B A C').
Lemma obtuse_not_acute : forall A B C, Obtuse A B C -> ~ Acute A B C.
Lemma acute_not_obtuse : forall A B C, Acute A B C -> ~ Obtuse A B C.
Lemma perp_obtuse_bet : forall A B C C', Perp A B C C' -> Col A B C' -> Obtuse A B C -> Bet A B C'.
Lemma lcos_const0 : forall l lp a, Lcos lp l a -> Q_CongA_Null_Acute a -> exists A, exists B, exists C, l A B /\ lp B C /\ a A B C.
Lemma lcos_const1 : forall l lp a P, Lcos lp l a -> ~ Q_CongA_Null_Acute a -> exists A, exists B, exists C, ~Col A B P /\ OS A B C P /\ l A B /\ lp B C /\ a A B C.
Lemma lcos_const : forall lp l a, Lcos lp l a -> exists A, exists B, exists C, lp A B /\ l B C /\ a A B C.
Lemma lcos_lg_distincts : forall lp l a A B C, Lcos lp l a -> l A B -> lp B C -> a A B C -> A <> B /\ C <> B.
Lemma lcos_const_a : forall lp l a B, Lcos lp l a -> exists A, exists C, l A B /\ lp B C /\ a A B C.
Lemma lcos_const_ab : forall lp l a B A, Lcos lp l a -> l A B -> exists C, lp B C /\ a A B C.
Lemma lcos_const_cb : forall lp l a B C, Lcos lp l a -> lp B C -> exists A, l A B /\ a A B C.
Lemma lcos_lg_anga : forall l lp a, Lcos lp l a -> Lcos lp l a /\ Q_Cong l /\ Q_Cong lp /\ Q_CongA_Acute a.
Lemma lcos_eql_lcos : forall lp1 l1 lp2 l2 a, EqL lp1 lp2 -> EqL l1 l2 -> Lcos lp1 l1 a -> Lcos lp2 l2 a.