Section OutputGreatestId.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {lmi : log_matching_interface}.
Context {si : sorted_interface}.
Context {aemi : applied_entries_monotonic_interface}.
Context {smsi : state_machine_safety_interface}.
Context {misi : max_index_sanity_interface}.
Context {smci : state_machine_correct_interface}.
Context {lacimi : lastApplied_commitIndex_match_interface}.

Lemma in_output_changed :
forall client id tr o,
~ key_in_output_trace client id tr ->
key_in_output_trace client id (tr ++ o) ->
key_in_output_trace client id o.