Definition HalfA P A O B := ~ Bet A O B /\ InAngle P A O B /\ CongA A O P B O P.

Lemma conga_halfa__conga1 : forall P A O B P' A' O' B', HalfA P A O B -> HalfA P' A' O' B' -> CongA A O P A' O' P' -> CongA A O B A' O' B'.