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. *)
Definition gHalfA A' O' B' A O B := exists P, HalfA P A O B /\ CongA A' O' B' A O P.
(** Given two angles a and b, a/2 = b/2 -> a = b *)
(** Given two angles a and b, a = b -> a/2 = b/2 *)
(** Unicity of the double angle *)

Lemma ghalfa2__conga_1 : forall A B C A' B' C' A'' B'' C'',
gHalfA A B C A' B' C' -> gHalfA A B C A'' B'' C'' -> CongA A' B' C' A'' B'' C''.