X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_constructors.ma;h=f263e2d140464896573bd1fddc5ebceaa2e322db;hb=829e3a8af3229c4e625245f7265dd67939da98c4;hp=31f4bbc14b306af1e227e1acab1afe8c93242bc9;hpb=b15b3e2d9e333bf94677ff2731c825da3566c9ec;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 31f4bbc14..f263e2d14 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,26 +12,43 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
-include "delayed_updating/syntax/prototerm_constructors.ma".
+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_iref_sn (f) (t:prototerm) (n:pnat):
-      (𝛗f@❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
-#f #t #n #p * #q * #r #Hr #H1 #H2 destruct
-@(ex2_intro … (𝗱n◗𝗺◗r))
+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_iref_dx (f) (t) (n:pnat):
-      ↑[f](𝛗n.t) ⊆ 𝛗f@❨n❩.↑[⇂*[n]f]t.
-#f #t #n #p * #q #Hq #H0 destruct
+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
-/3 width=1 by in_comp_iref, in_comp_lift_bi/
+<lift_path_d_sn <lift_path_m_sn
+/3 width=1 by in_comp_iref, in_comp_lift_path_term/
 qed-.
 
-lemma lift_iref (f) (t) (n:pnat):
-      (𝛗f@❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
-/3 width=1 by conj, lift_iref_sn, lift_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).
+#t #n #k
+@(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.