Definition minimal_contradicting_leader_log net t e :=
    argmin (fun l => fst (fst l)) (contradicting_leader_logs net nodes t e).

Lemma contradicting_leader_logs_complete : forall net nodes h t e l t', In h nodes -> In (t', l) (contradicting_leader_logs_on_leader (leaderLogs (fst (nwState net h))) t e) -> In (t', h, l) (contradicting_leader_logs net nodes t e).