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_distincts : forall P A O B, HalfA P A O B -> O <> A /\ O <> B /\ O <> P.