X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Funwind%2Funwind2_rmap_closed.ma;h=b0d062de63b8dc18ef33d422531c793d28cee4d2;hb=119da3f9ce130f7c4e8b23fcc491d221472ad657;hp=7c551ed857d82aebe819bd896f23fc8dd02079e9;hpb=829e3a8af3229c4e625245f7265dd67939da98c4;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
index 7c551ed85..b0d062de6 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
@@ -16,6 +16,7 @@ include "delayed_updating/unwind/unwind2_rmap_eq.ma".
 include "delayed_updating/syntax/path_closed.ma".
 include "delayed_updating/syntax/path_depth.ma".
 include "ground/relocation/xap.ma".
+include "ground/lib/stream_tls_plus.ma".
 include "ground/lib/stream_eq_eq.ma".
 include "ground/arith/nat_le_plus.ma".
 include "ground/arith/nat_le_pred.ma".
@@ -24,11 +25,11 @@ include "ground/arith/nat_le_pred.ma".
 
 (* Destructions with cpp ****************************************************)
 
-lemma unwind2_rmap_append_closed_dx_xap_le (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ → ∀m. m ≤ n →
+lemma xap_le_unwind2_rmap_append_closed_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ → ∀m. m ≤ n →
       ▶[f]q＠❨m❩ = ▶[f](p●q)＠❨m❩.
-#f #p #q #n #Hq elim Hq -q -n
-[|*: #q #n [ #k ] #_ #IH ] #m #Hm
+#o #f #p #q #n #Hq elim Hq -q -n
+[|*: #q #n [ #k #_ ] #_ #IH ] #m #Hm
 [ <(nle_inv_zero_dx … Hm) -m //
 | <unwind2_rmap_d_dx <unwind2_rmap_d_dx
   <tr_compose_xap <tr_compose_xap
@@ -48,45 +49,95 @@ lemma unwind2_rmap_append_closed_dx_xap_le (f) (p) (q) (n):
 ]
 qed-.
 
-lemma unwind2_rmap_append_L_closed_dx_nap (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ →
+lemma nap_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
       ▶[f](𝗟◗q)＠§❨n❩ = ▶[f](p●𝗟◗q)＠§❨n❩.
-#f #p #q #n #Hq
+#o #f #p #q #n #Hq
 lapply (pcc_L_sn … Hq) -Hq #Hq
-lapply (unwind2_rmap_append_closed_dx_xap_le f p … Hq (↑n) ?) -Hq //
+lapply (xap_le_unwind2_rmap_append_closed_dx o f p … Hq (↑n) ?) -Hq //
 <tr_xap_succ_nap <tr_xap_succ_nap #Hq
 /2 width=1 by eq_inv_nsucc_bi/
 qed-.
 
-lemma unwind2_rmap_push_closed_nap (f) (q) (n):
-      q ϵ 𝐂❨n❩ →
+lemma nap_unwind2_rmap_push_closed_depth (o) (f) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
       ♭q = ▶[⫯f]q＠§❨n❩.
-#f #q #n #Hq elim Hq -q -n
-[|*: #q #n [ #k ] #_ #IH ] //
+#o #f #q #n #Hq elim Hq -q -n
+[|*: #q #n [ #k #_ ] #_ #IH ] //
 <unwind2_rmap_d_dx <tr_compose_nap //
 qed-.
 
-lemma unwind2_rmap_append_closed_nap (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ →
+lemma nap_unwind2_rmap_append_closed_Lq_dx_depth (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
       ♭q = ▶[f](p●𝗟◗q)＠§❨n❩.
-#f #p #q #n #Hq
-<unwind2_rmap_append_L_closed_dx_nap //
-/2 width=1 by unwind2_rmap_push_closed_nap/
+#o #f #p #q #n #Hq
+<nap_unwind2_rmap_append_closed_Lq_dx //
+/2 width=2 by nap_unwind2_rmap_push_closed_depth/
 qed-.
 
-lemma tls_succ_plus_unwind2_rmap_push_closed (f) (q) (n):
-      q ϵ 𝐂❨n❩ →
+lemma xap_unwind2_rmap_append_closed_true_dx_depth (f) (p) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ → ♭q = ▶[f](p●q)＠❨n❩.
+#f #p #q #n #Hq elim Hq -q -n //
+#q #n #k #Ho #_ #IH
+<unwind2_rmap_d_dx <tr_compose_xap
+>Ho // <tr_uni_xap_succ <Ho //
+qed-.
+
+lemma tls_succ_plus_unwind2_rmap_push_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 //
+#q #n #k #_ #_ #IH #m
+@(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+>nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
+qed-.
+
+lemma tls_plus_unwind2_rmap_closed_true (f) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ →
+      ∀m. ⇂*[m]f ≗ ⇂*[m+n]▶[f]q.
 #f #q #n #Hq elim Hq -q -n //
-#q #n [ #k ] #_ #IH #m
-[ @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
-  >nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
-| <unwind2_rmap_L_dx <nplus_succ_dx //
-]
+#q #n #k #Ho #_ #IH #m
+>Ho // <nplus_succ_dx
+@(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+>nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold
+>nplus_succ_dx <Ho //
 qed-.
 
-lemma tls_succ_unwind2_rmap_append_L_closed_dx (f) (p) (q) (n):
-      q ϵ 𝐂❨n❩ →
+lemma tls_succ_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
+      q ϵ 𝐂❨o,n❩ →
       ▶[f]p ≗ ⇂*[↑n]▶[f](p●𝗟◗q).
-/2 width=1 by tls_succ_plus_unwind2_rmap_push_closed/
+/2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
+qed-.
+
+lemma tls_unwind2_rmap_append_closed_true_dx (f) (p) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ →
+      ▶[f]p ≗ ⇂*[n]▶[f](p●q).
+/2 width=1 by tls_plus_unwind2_rmap_closed_true/
+qed-.
+
+lemma nap_plus_unwind2_rmap_append_closed_Lq_dx_depth (o) (f) (p) (q) (m) (n):
+      q ϵ 𝐂❨o,n❩ →
+      ▶[f]p＠❨m❩+♭q = ▶[f](p●𝗟◗q)＠§❨m+n❩.
+#o #f #p #q #m #n #Hq
+<tr_nap_plus @eq_f2
+[ <(tr_xap_eq_repl … (tls_succ_unwind2_rmap_append_closed_Lq_dx …)) //
+| /2 width=2 by nap_unwind2_rmap_append_closed_Lq_dx_depth/
+]
+qed-.
+
+lemma nap_plus_unwind2_rmap_append_closed_bLq_dx_depth (o) (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨Ⓣ,m❩ → q ϵ 𝐂❨o,n❩ →
+      ♭b+♭q = ▶[f](p●b●𝗟◗q)＠§❨m+n❩.
+#o #f #p #b #q #m #n #Hb #Hq
+>(xap_unwind2_rmap_append_closed_true_dx_depth f p … Hb) -Hb
+>(nap_plus_unwind2_rmap_append_closed_Lq_dx_depth … Hq) -Hq //
+qed-.
+
+lemma tls_succ_plus_unwind2_rmap_append_closed_bLq_dx (o) (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨Ⓣ,m❩ → q ϵ 𝐂❨o,n❩ →
+      ▶[f]p ≗ ⇂*[↑(m+n)]▶[f](p●b●𝗟◗q).
+#o #f #p #b #q #m #n #Hb #Hq
+>nplus_succ_dx <stream_tls_plus >list_append_assoc
+@(stream_eq_trans … (tls_unwind2_rmap_append_closed_true_dx … Hb)) -Hb
+/3 width=2 by stream_tls_eq_repl, tls_succ_unwind2_rmap_append_closed_Lq_dx/
 qed-.