End Tarski_neutral_to_Euclid_neutral.
Section circle_continuity.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma bet_cases : forall B C D1 D2,
C<>B ->
Definitions.BetS D1 B D2 ->
Definitions.BetS D1 C D2 ->
Definitions.BetS D1 B C \/ Definitions.BetS C B D2.
Lemma circle_line :
circle_circle ->
forall A B C K P Q,
CI K C P Q -> InCirc B K ->  A <> B ->
exists X Y, Definitions.Col A B X /\ Definitions.Col A B Y /\
OnCirc X K /\ OnCirc Y K /\ Definitions.BetS X B Y.
Lemma circle_circle' :
circle_circle ->
forall C D F G J K P Q R S,
CI J C R S -> InCirc P J ->
OutCirc Q J -> CI K D F G ->
OnCirc P K -> OnCirc Q K ->
exists X, OnCirc X J /\ OnCirc X K.