X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_rmap_closed.ma;h=ec386108eded9b3ab11c994a8d6b8fd0fa6d70d4;hp=cc3e61bf7c5ebcfbf3097bff72a55b87e966c070;hb=119da3f9ce130f7c4e8b23fcc491d221472ad657;hpb=829e3a8af3229c4e625245f7265dd67939da98c4

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
index cc3e61bf7..ec386108e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
@@ -14,30 +14,52 @@
 
 include "delayed_updating/substitution/lift_rmap_eq.ma".
 include "delayed_updating/syntax/path_closed.ma".
+include "ground/relocation/xap.ma".
 include "ground/lib/stream_eq_eq.ma".
 
 (* LIFT MAP FOR PATH ********************************************************)
 
 (* Destructions with cpp ****************************************************)
 
-lemma tls_plus_lift_rmap_closed (f) (q) (n):
-      q ϵ 𝐂❨n❩ →
-      ∀m. ⇂*[m]f ≗ ⇂*[m+n]↑[q]f.
-#f #q #n #Hq elim Hq -q -n //
-#q #n #_ #IH #m
-<nplus_succ_dx <stream_tls_swap //
+lemma tls_plus_lift_rmap_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
+      ∀m. ⇂*[m]f ≗ ⇂*[m+n]🠢[f]q.
+#o #f #q #n #Hq elim Hq -q -n //
 qed-.
 
-lemma tls_lift_rmap_closed (f) (q) (n):
-      q ϵ 𝐂❨n❩ →
-      f ≗ ⇂*[n]↑[q]f.
-#f #q #n #H0
-/2 width=1 by tls_plus_lift_rmap_closed/
+lemma tls_lift_rmap_closed (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
+      f ≗ ⇂*[n]🠢[f]q.
+#o #f #q #n #H0
+/2 width=2 by tls_plus_lift_rmap_closed/
 qed-.
 
-lemma tls_succ_lift_rmap_append_L_closed_dx (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ →
-      ↑[p]f ≗ ⇂*[↑n]↑[p●𝗟◗q]f.
-#f #p #q #n #Hq
-/3 width=1 by tls_lift_rmap_closed, pcc_L_sn/
+lemma tls_lift_rmap_append_closed_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
+      🠢[f]p ≗ ⇂*[n]🠢[f](p●q).
+#o #f #p #q #n #Hq
+/2 width=2 by tls_lift_rmap_closed/
+qed-.
+
+lemma tls_succ_lift_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
+      🠢[f]p ≗ ⇂*[↑n]🠢[f](p●𝗟◗q).
+#o #f #p #q #n #Hq
+/3 width=2 by tls_lift_rmap_append_closed_dx, pcc_L_sn/
+qed-.
+
+lemma tls_succ_plus_lift_rmap_append_closed_bLq_dx (o1) (o2) (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨o1,m❩ → q ϵ 𝐂❨o2,n❩ →
+      🠢[f]p ≗ ⇂*[↑(m+n)]🠢[f](p●b●𝗟◗q).
+#o1 #o2 #f #p #b #q #m #n #Hm #Hn
+>nplus_succ_dx <stream_tls_plus
+@(stream_eq_trans … (tls_lift_rmap_append_closed_dx … Hm))
+/3 width=2 by stream_tls_eq_repl, tls_succ_lift_rmap_append_closed_Lq_dx/
+qed-.
+
+lemma nap_plus_lift_rmap_append_closed_Lq_dx (o) (f) (p) (q) (m) (n):
+      q ϵ 𝐂❨o,n❩ →
+      🠢[f](p)＠❨m❩+🠢[f](p●𝗟◗q)＠§❨n❩ = 🠢[f](p●𝗟◗q)＠§❨m+n❩.
+#o #f #p #q #m #n #Hq
+/4 width=2 by eq_f2, tr_xap_eq_repl, tls_succ_lift_rmap_append_closed_Lq_dx/
 qed-.