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

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.