Instance same_covered_eq {ora: RandomOracle}: Equivalence same_covered_anti_chain.

Lemma proj_in_anti_chain_unique {ora: RandomOracle}: forall (d: HistoryAntiChain) h1 h2 h3,
prefix_history h1 h3 ->
prefix_history h2 h3 ->
covered_by h2 d ->
d h1 ->
prefix_history h1 h2.