Require Export GeoCoq.Tarski_dev.Ch12_parallel.
Section Circle.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma inc112 : forall A B,
InCircle A A B.
Lemma onc212 : forall A B,
OnCircle B A B.
Lemma onc_sym : forall A B P, OnCircle P A B -> OnCircle B A P.
Lemma ninc__outcs : forall X O P, ~ InCircle X O P -> OutCircleS X O P.
Lemma inc__outc : forall A B P, InCircle P A B <-> OutCircle B A P.
Lemma incs__outcs : forall A B P, InCircleS P A B <-> OutCircleS B A P.
Lemma onc__inc : forall A B P, OnCircle P A B -> InCircle P A B.
Lemma onc__outc : forall A B P, OnCircle P A B -> OutCircle P A B.
Lemma inc_outc__onc : forall A B P, InCircle P A B -> OutCircle P A B -> OnCircle P A B.
Lemma incs__inc : forall A B P, InCircleS P A B -> InCircle P A B.
Lemma outcs__outc : forall A B P, OutCircleS P A B -> OutCircle P A B.
Lemma incs__noutc : forall A B P, InCircleS P A B <-> ~ OutCircle P A B.
Lemma outcs__ninc : forall A B P, OutCircleS P A B <-> ~ InCircle P A B.
Lemma inc__noutcs : forall A B P, InCircle P A B <-> ~ OutCircleS P A B.
Lemma outc__nincs : forall A B P, OutCircle P A B <-> ~ InCircleS P A B.
Lemma inc_eq : forall A P, InCircle P A A -> A = P.
Lemma outc_eq : forall A B, OutCircle A A B -> A = B.
Lemma onc2__cong : forall O P A B, OnCircle A O P -> OnCircle B O P -> Cong O A O B.
End Circle.