(* Gabriel Braun April 2013 *)
Require Export GeoCoq.Tarski_dev.Ch13_3_angles.
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.
Section Cosinus.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(************************************* cos *****************************)

(* 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'.
End Cosinus.