Definition limit_domain_anti_chain (Omegas: RandomVarDomainStream): HistoryAntiChain := Build_HistoryAntiChain _ (limit_raw_domain Omegas) (limit_raw_domain_legal Omegas).

Lemma limit_domain_anti_chain_hered: forall (Omegas: RandomVarDomainStream) (n: nat) h, Omegas n h -> exists h_limit, prefix_history h h_limit /\ limit_domain_anti_chain Omegas h_limit.