Definition is_max_anti_chain {ora: RandomOracle} (d: HistoryAntiChain): Prop :=
forall h, is_inf_history h ->
exists h', (prefix_history h' h \/ strict_conflict_history h' h) /\ d h'.

Lemma unit_anti_chain_max {ora: RandomOracle}: is_max_anti_chain unit_space_anti_chain.