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 lta_nbet__ncol : forall A B C X Y Z, ~ Bet X Y Z -> LtA A B C X Y Z -> ~ Col X Y Z. *)

Lemma inangle_halfa2__inangle : forall O A B C A' C',
~ Col A O B -> InAngle C A O B ->
HalfA A' A O B -> HalfA C' C O B ->
InAngle C' A' O B.