update in delayd_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index e87ccb21f0cb641bb48f4cf6ee666e8bc1ec455e..f263e2d140464896573bd1fddc5ebceaa2e322db 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -15,17 +15,18 @@
 include "delayed_updating/substitution/lift_prototerm_id.ma".
 include "delayed_updating/substitution/lift_path_uni.ma".
 include "delayed_updating/syntax/prototerm_constructors_eq.ma".
+include "ground/relocation/nap.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
-lemma lift_term_iref_sn (f) (t:prototerm) (k:pnat):
+lemma lift_term_iref_pap_sn (f) (t:prototerm) (k:pnat):
       (𝛕f＠⧣❨k❩.↑[⇂*[k]f]t) ⊆ ↑[f](𝛕k.t).
 #f #t #k #p * #q * #r #Hr #H1 #H2 destruct
 @(ex2_intro … (𝗱k◗𝗺◗r))
 /2 width=1 by in_comp_iref/
 qed-.
 
-lemma lift_term_iref_dx (f) (t) (k:pnat):
+lemma lift_term_iref_pap_dx (f) (t) (k:pnat):
       ↑[f](𝛕k.t) ⊆ 𝛕f＠⧣❨k❩.↑[⇂*[k]f]t.
 #f #t #k #p * #q #Hq #H0 destruct
 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
@@ -33,15 +34,21 @@ elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
 /3 width=1 by in_comp_iref, in_comp_lift_path_term/
 qed-.
 
-lemma lift_term_iref (f) (t) (k:pnat):
+lemma lift_term_iref_pap (f) (t) (k:pnat):
       (𝛕f＠⧣❨k❩.↑[⇂*[k]f]t) ⇔ ↑[f](𝛕k.t).
-/3 width=1 by conj, lift_term_iref_sn, lift_term_iref_dx/
+/3 width=1 by conj, lift_term_iref_pap_sn, lift_term_iref_pap_dx/
+qed.
+
+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 …))
+@(subset_eq_trans … (lift_term_iref_pap …))
 <tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
 /3 width=1 by iref_eq_repl, lift_term_id/
 qed.