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

Lemma halfa2_lta__lta2 : forall P A O B P' A' O' B', HalfA P A O B -> HalfA P' A' O' B' -> LtA A' O' B' A O B -> LtA A' O' P' A O P.