Proof using.
start.
find_apply_lem_hyp doLeader_type. intuition; try congruence.
match goal with
| [ H : forall _, _ -> exists _, _, h : name |- _ ] =>
specialize (H h)
end.
repeat find_rewrite. eauto.
Qed.

(* Specifications: *)
Lemma leaders_have_leaderLogs_strong_init :
refined_raft_net_invariant_init leaders_have_leaderLogs_strong.
Lemma leaders_have_leaderLogs_init :
refined_raft_net_invariant_init leaders_have_leaderLogs.