-lemma lift_iref_uni (t) (m) (n):
- (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
-#t #m #n
-@(subset_eq_trans … (lift_iref …))
+lemma lift_term_iref_nap (f) (t) (n):
+ (𝛕↑(f@§❨n❩).↑[⇂*[↑n]f]t) ⇔ ↑[f](𝛕↑n.t).
+#f #t #n
+>tr_pap_succ_nap //
+qed.
+
+lemma lift_term_iref_uni (t) (n) (k):
+ (𝛕(k+n).t) ⇔ ↑[𝐮❨n❩](𝛕k.t).
+#t #n #k
+@(subset_eq_trans … (lift_term_iref_pap …))