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 out_preserves_halfa : forall P A O B P' A' B',
Out O A A' -> Out O B B' -> Out O P P' ->
HalfA P A O B -> HalfA P' A' O B'.