update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind / unwind2_rmap_head.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
index cd21acf66ae962333918f0a426ad930587ed1872..f6fbae1811b75ae42b924e78c0fda631b42c2200 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
@@ -24,38 +24,38 @@ include "ground/arith/nat_le_plus.ma".
 (* Constructions with path_head *********************************************)
 
 lemma unwind2_rmap_head_xap_le_closed (f) (p) (q) (n) (k):
-      p = (↳[n]p)●q → k ≤ n →
-      (▶[f]p)＠❨k❩ = (▶[f]↳[n]p)＠❨k❩.
+      p = ↳[n]p → k ≤ n →
+      ▶[f](p●q)＠❨k❩ = ▶[f]↳[n](p●q)＠❨k❩.
 #f #p elim p -p
-[ #q #n #k #Hq #Hk
-  elim (eq_inv_list_empty_append … Hq) -Hq * #_ //
+[ #q #n #k #Hq
+  <(eq_inv_path_empty_head … Hq) -n #Hk
+  <(nle_inv_zero_dx … Hk) -k //
 | #l #p #IH #q #n @(nat_ind_succ … n) -n
-  [ #k #_ #Hk <(nle_inv_zero_dx … Hk) -k -IH
-   <path_head_zero <unwind2_rmap_empty //
+  [ #k #_ #Hk <(nle_inv_zero_dx … Hk) -k -IH //
   | #n #_ #k cases l [ #m ]
-    [ <path_head_d_sn <list_append_lcons_sn #Hq #Hk
+    [ <path_head_d_sn #Hq #Hk
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
       <unwind2_rmap_d_sn <unwind2_rmap_d_sn
       <tr_compose_xap <tr_compose_xap
       @(IH … Hq) -IH -Hq (**) (* auto too slow *)
       @nle_trans [| @tr_uni_xap ]
       /2 width=1 by nle_plus_bi_dx/
-    | <path_head_m_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_m_sn #Hq #Hk
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
       <unwind2_rmap_m_sn <unwind2_rmap_m_sn
       /2 width=2 by/
-    | <path_head_L_sn <list_append_lcons_sn #Hq
+    | <path_head_L_sn #Hq
       @(nat_ind_succ … k) -k // #k #_ #Hk
       lapply (nle_inv_succ_bi … Hk) -Hk #Hk
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
       <unwind2_rmap_L_sn <unwind2_rmap_L_sn
       <tr_xap_push <tr_xap_push
       /3 width=2 by eq_f/
-    | <path_head_A_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_A_sn #Hq #Hk
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
       <unwind2_rmap_A_sn <unwind2_rmap_A_sn
       /2 width=2 by/
-    | <path_head_S_sn <list_append_lcons_sn #Hq #Hk
+    | <path_head_S_sn #Hq #Hk
       elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
       <unwind2_rmap_S_sn <unwind2_rmap_S_sn
       /2 width=2 by/
@@ -64,8 +64,8 @@ lemma unwind2_rmap_head_xap_le_closed (f) (p) (q) (n) (k):
 ]
 qed-.
 
-lemma unwind2_rmap_head_append_xap_closed (f) (p) (q) (n):
-      p = ↳[n](p●q) →
+lemma unwind2_rmap_head_xap_closed (f) (p) (q) (n):
+      p = ↳[n]p →
       ▶[f](p●q)＠❨n❩ = ▶[f]↳[n](p●q)＠❨n❩.
 /2 width=2 by unwind2_rmap_head_xap_le_closed/
 qed-.
@@ -89,47 +89,45 @@ lemma unwind2_rmap_head_xap (f) (p) (n):
 qed.
 
 lemma unwind2_rmap_append_pap_closed (f) (p) (q) (n:pnat):
-      p = ↳[n](p●q) →
+      p = ↳[n]p →
       ♭p = ninj (▶[f](p●q)＠⧣❨n❩).
 #f #p #q #n #Hn
->tr_xap_ninj >Hn in ⊢ (??%?);
->(unwind2_rmap_head_append_xap_closed … Hn) -Hn
+>tr_xap_ninj >(path_head_refl_append q … Hn) in ⊢ (??%?); 
+>(unwind2_rmap_head_xap_closed … Hn) -Hn
 <path_head_depth //
 qed.
 
 lemma tls_unwind2_rmap_plus_closed (f) (p) (q) (n) (k):
-      p = (↳[n]p)●q →
-      ⇂*[k]▶[f]q ≗ ⇂*[n+k]▶[f]p.
+      p = ↳[n]p →
+      ⇂*[k]▶[f]q ≗ ⇂*[n+k]▶[f](p●q).
 #f #p elim p -p
 [ #q #n #k #Hq
-  elim (eq_inv_list_empty_append … Hq) -Hq #Hn #H0 destruct
-  <path_head_empty in Hn; #Hn
-  <(eq_inv_empty_labels … Hn) -n //
+  <(eq_inv_path_empty_head … Hq) -n //
 | #l #p #IH #q #n @(nat_ind_succ … n) -n //
   #n #_ #k cases l [ #m ]
-  [ <path_head_d_sn <list_append_lcons_sn #Hq
+  [ <path_head_d_sn #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq <nrplus_inj_sn
     @(stream_eq_trans … (tls_unwind2_rmap_d_sn …))
     >nrplus_inj_dx >nrplus_inj_sn >nrplus_inj_sn <nplus_plus_comm_23
     /2 width=1 by/
-  | <path_head_m_sn <list_append_lcons_sn #Hq
+  | <path_head_m_sn #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
     <unwind2_rmap_m_sn /2 width=1 by/
-  | <path_head_L_sn <list_append_lcons_sn #Hq
+  | <path_head_L_sn #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
     <unwind2_rmap_L_sn <nplus_succ_sn /2 width=1 by/
-  | <path_head_A_sn <list_append_lcons_sn #Hq
+  | <path_head_A_sn #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
     <unwind2_rmap_A_sn /2 width=2 by/
-  | <path_head_S_sn <list_append_lcons_sn #Hq
+  | <path_head_S_sn #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
     <unwind2_rmap_S_sn /2 width=2 by/
   ]
 ]
 qed-.
 
-lemma tls_unwind2_rmap_append_closed (f) (p) (q) (n):
-      p = ↳[n](p●q) →
+lemma tls_unwind2_rmap_closed (f) (p) (q) (n):
+      p = ↳[n]p →
       ▶[f]q ≗ ⇂*[n]▶[f](p●q).
 /2 width=1 by tls_unwind2_rmap_plus_closed/
 qed.