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(* Specifications: *)
Lemma lcos3_eq_refl : forall l a b c, Q_Cong l -> ~ Q_Cong_Null l -> Q_CongA_Acute a -> Q_CongA_Acute b -> Q_CongA_Acute c -> Eq_Lcos3 l a b c l a b c.
Lemma lcos3_eq_sym : forall l1 a b c l2 d e f, Eq_Lcos3 l1 a b c l2 d e f -> Eq_Lcos3 l2 d e f l1 a b c.
Lemma lcos3_uniqueness: forall l l1 l2 a b c, Lcos3 l1 l a b c -> Lcos3 l2 l a b c -> EqL l1 l2.
Lemma lcos3_eql_lcos3 : forall lla llb la lb a b c, Lcos3 la lla a b c -> EqL lla llb -> EqL la lb -> Lcos3 lb llb a b c.
Lemma lcos3_lg_anga : forall lp l a b c, Lcos3 lp l a b c -> Lcos3 lp l a b c /\ Q_Cong lp /\ Q_Cong l /\ Q_CongA_Acute a /\ Q_CongA_Acute b /\ Q_CongA_Acute c.
Lemma lcos3_lg_not_null: forall lp l a b c, Lcos3 lp l a b c -> ~ Q_Cong_Null l /\ ~ Q_Cong_Null lp.
Lemma lcos3_eq_trans : forall l1 a b c l2 d e f l3 g h i,
Eq_Lcos3 l1 a b c l2 d e f -> Eq_Lcos3 l2 d e f l3 g h i -> Eq_Lcos3 l1 a b c l3 g h i.
Lemma lcos_eq_lcos3_eq : forall la lb a b c d, Q_CongA_Acute c -> Q_CongA_Acute d -> Eq_Lcos la a lb b -> Eq_Lcos3 la a c d lb b c d.
Lemma lcos2_eq_lcos3_eq : forall la lb a b c d e, Q_CongA_Acute e -> Eq_Lcos2 la a b lb c d -> Eq_Lcos3 la a b e lb c d e.
End Cosinus2.