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 0202dc9264c50cf0cc99216fbe0eafe7d9d01edf..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
@@ -12,45 +12,43 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_eq.ma".
-
-axiom lift_path_after (p) (f1) (f2):
-      ↑[f2]↑[f1]p = ↑[f2∘f1]p.
-(*
-#p @(path_ind_lift … p) -p // [ #n | #n #l #p | #p ] #IH #f1 #f2
-[ <lift_path_d_empty_sn <lift_path_d_empty_sn
-| <lift_path_d_lcons_sn <lift_path_d_lcons_sn
-| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
-*)
-include "delayed_updating/substitution/lift_prototerm.ma".
-
-axiom lift_term_after (t) (f1) (f2):
-      ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
-
-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_after_sn (f) (t) (n:pnat):
-      ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
-#f #t #n #p * #q #Hq #H0 destruct
-@(ex2_intro … (𝗱n◗𝗺◗q))
+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_after_dx (f) (t) (n:pnat):
-      ↑[f](𝛗n.t) ⊆ ↑[f∘𝐮❨n❩]t.
-#f #t #n #p * #q #Hq #H0 destruct
-elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
-/2 width=1 by in_comp_lift_bi/
+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_iref_after (f) (t) (n:pnat):
-      ↑[f∘𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
-/3 width=1 by conj, lift_iref_after_sn, lift_iref_after_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_iref (f) (t) (n:pnat):
-      ↑[f]↑[𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
-/3 width=3 by lift_term_after, subset_eq_trans/
+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.