update in delayed_updating

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

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 56abc470717544ad2e53d3aa681608f48a349dcf..ec386108eded9b3ab11c994a8d6b8fd0fa6d70d4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
@@ -14,6 +14,7 @@
 
 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 ********************************************************)
@@ -22,22 +23,43 @@ include "ground/lib/stream_eq_eq.ma".
 
 lemma tls_plus_lift_rmap_closed (o) (f) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      ∀m. ⇂*[m]f ≗ ⇂*[m+n]↑[q]f.
+      ∀m. ⇂*[m]f ≗ ⇂*[m+n]🠢[f]q.
 #o #f #q #n #Hq elim Hq -q -n //
-#q #n #_ #IH #m
-<nplus_succ_dx <stream_tls_swap //
 qed-.
 
 lemma tls_lift_rmap_closed (o) (f) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      f ≗ ⇂*[n]↑[q]f.
+      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 (o) (f) (p) (q) (n):
+lemma tls_lift_rmap_append_closed_dx (o) (f) (p) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      ↑[p]f ≗ ⇂*[↑n]↑[p●𝗟◗q]f.
+      🠢[f]p ≗ ⇂*[n]🠢[f](p●q).
 #o #f #p #q #n #Hq
-/3 width=2 by tls_lift_rmap_closed, pcc_L_sn/
+/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-.