proposition: Lemma ghalfa_distincts : forall A' O' B' A O B, gHalfA A' O' B' A O B -> O' <> A' /\ O' <> B' /\ O <> A /\ O <> B.
proof: Proof. intros A' O' B' A O B [P [HP]]. apply halfa_distincts in HP. spliter. assert_diffs. repeat split; auto. Qed.
imports: GeoCoq.Tarski_dev.Annexes.suma