Section HalfAngle.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition HalfA P A O B := ~ Bet A O B /\ InAngle P A O B /\ CongA A O P B O P.

Lemma halfa__nbet2 : forall A O B P, HalfA P A O B -> ~ Bet A O P /\ ~ Bet B O P.