Global Instance eqA_equivalence : Equivalence EqA.

(* Specifications: *)
Lemma null_anga : forall A B C D a1 a2, Ang_Acute A B A a1 -> Ang_Acute C D C a2 -> EqA a1 a2.
Lemma anga_distinct: forall a A B C, Q_CongA_Acute a -> a A B C -> A <> B /\ C <> B.
Lemma out_is_len_eq : forall A B C l, Out A B C -> Len A B l -> Len A C l -> B = C.
Lemma out_len_eq : forall A B C l, Q_Cong l -> Out A B C -> l A B -> l A C -> B = C.
Lemma ex_anga : forall A B C, Acute A B C -> exists a, Q_CongA_Acute a /\ a A B C.
Lemma not_null_ang_ang : forall a, Q_CongA_nNull a -> Q_CongA a.
Lemma not_null_ang_def_equiv : forall a, Q_CongA_nNull a <-> (Q_CongA a /\ exists A, exists B, exists C, a A B C /\ ~Out B A C).
Lemma not_flat_ang_def_equiv : forall a, Q_CongA_nFlat a <-> (Q_CongA a /\ exists A, exists B, exists C, a A B C /\ ~Bet A B C).
Lemma ang_const : forall a A B, Q_CongA a -> A <> B -> exists C, a A B C.