Section inner.
Variable client : clientId.
Variable id : nat.
Variable i : input.
Proof using.
unfold applied_implies_input_state.
intros.
break_exists_exists.
intuition.
break_exists.
simpl in *.
destruct (name_eq_dec h x0); rewrite_update; eauto.
Qed.
Proof using.
unfold applied_implies_input_state.
eauto 10.
Qed.
Proof using.
unfold applied_implies_input_state.
eauto 10.
Qed.
Proof using.
intros. unfold doGenericServer in *.
repeat break_match; find_inversion;
use_applyEntries_spec; simpl in *;
subst; auto.
Qed.
Proof using.
intros. unfold handleTimeout, tryToBecomeLeader in *.
break_match; find_inversion; subst; auto.
Qed.
Proof using.
unfold handleClientRequest.
intros.
break_match; find_inversion; simpl in *; intuition.
Qed.

Lemma mEntries_some_is_applied_entries :
forall m es,
mEntries m = Some es ->
is_append_entries m.