X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_constructors.ma;h=56f7b178a5400eda07f3e99156ee475719629b46;hb=48cd63fc7f4415925582eae224a36a9c1bb3cc06;hp=e87ccb21f0cb641bb48f4cf6ee666e8bc1ec455e;hpb=5c2d38b46908f662cbb717156b29101ff30f8352;p=helm.git

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 e87ccb21f..56f7b178a 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -15,33 +15,40 @@
 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):
-      (𝛕f＠⧣❨k❩.↑[⇂*[k]f]t) ⊆ ↑[f](𝛕k.t).
+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):
-      ↑[f](𝛕k.t) ⊆ 𝛕f＠⧣❨k❩.↑[⇂*[k]f]t.
+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
 <lift_path_d_sn <lift_path_m_sn
 /3 width=1 by in_comp_iref, in_comp_lift_path_term/
 qed-.
 
-lemma lift_term_iref (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/
+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_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).
+      (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.