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

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