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 cop_halfa_perp__os : forall P A O B T, HalfA P A O B -> Perp O P T O -> Coplanar A O P T ->
OS O T P A.