Proof using olpti rri.
intros.
eapply (lift_prop _ one_leader_per_term_invariant _ ltac:(eauto));
simpl in *; repeat break_match; repeat (find_rewrite; simpl in *);
auto; simpl in *; repeat find_rewrite; simpl in *; auto.
Qed.

Lemma map_snd :
forall {A B} (a : A) (b : B) l,
In (a, b) l ->
In b (map snd l).