commit in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
index 3dadf0fcd4385f6106d98f11703847949fd8cd52..033a2c13e1aafb768c50439213e3a2e77ab9af2e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
@@ -12,51 +12,46 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_gen_eq.ma".
+include "delayed_updating/substitution/lift_rmap_eq.ma".
 include "delayed_updating/syntax/path_head.ma".
-include "delayed_updating/syntax/path_reverse.ma".
 include "ground/lib/stream_eq_eq.ma".
 
 (* LIFT MAP FOR PATH ********************************************************)
 
 (* Constructions with path_head *********************************************)
 
-lemma tls_plus_lift_rmap_reverse_closed (f) (q) (p) (n) (k):
-      q = (↳[n]q)●p →
-      ⇂*[k]↑[pᴿ]f ≗ ⇂*[n+k]↑[qᴿ]f.
+lemma tls_plus_lift_rmap_closed (f) (q) (n) (m):
+      q = ↳[n]q →
+      ⇂*[m]f ≗ ⇂*[n+m]↑[q]f.
 #f #q elim q -q
-[ #p #n #k #Hp
-  elim (eq_inv_list_empty_append … Hp) -Hp #Hn #H0 destruct
-  <path_head_empty in Hn; #Hn
-  <(eq_inv_empty_labels … Hn) -n //
-| #l #q #IH #p #n @(nat_ind_succ … n) -n //
-  #n #_ #k cases l [ #m ]
-  [ <path_head_d_sn <list_append_lcons_sn #Hp
-    elim (eq_inv_list_lcons_bi ????? Hp) -Hp #_ #Hp <nrplus_inj_sn
-    <reverse_lcons
+[ #n #m #Hq
+  <(eq_inv_path_empty_head … Hq) -n //
+| #l #q #IH #n @(nat_ind_succ … n) -n //
+  #n #_ #m cases l [ #k ]
+  [ <path_head_d_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq <nrplus_inj_sn
     @(stream_eq_trans … (tls_lift_rmap_d_dx …))
     >nrplus_inj_dx >nrplus_inj_sn >nrplus_inj_sn <nplus_plus_comm_23
     >nsucc_unfold /2 width=1 by/
-  | <path_head_m_sn <list_append_lcons_sn #Hp
-    elim (eq_inv_list_lcons_bi ????? Hp) -Hp #_ #Hp
-    <reverse_lcons <lift_rmap_m_dx /2 width=1 by/
-  | <path_head_L_sn <list_append_lcons_sn #Hp
-    elim (eq_inv_list_lcons_bi ????? Hp) -Hp #_ #Hp
-    <reverse_lcons <lift_rmap_L_dx <nplus_succ_sn /2 width=1 by/
-  | <path_head_A_sn <list_append_lcons_sn #Hp
-    elim (eq_inv_list_lcons_bi ????? Hp) -Hp #_ #Hp
-    <reverse_lcons <lift_rmap_A_dx /2 width=2 by/
-  | <path_head_S_sn <list_append_lcons_sn #Hp
-    elim (eq_inv_list_lcons_bi ????? Hp) -Hp #_ #Hp
-    <reverse_lcons <lift_rmap_S_dx /2 width=2 by/
+  | <path_head_m_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_m_dx /2 width=1 by/
+  | <path_head_L_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_L_dx <nplus_succ_sn /2 width=1 by/
+  | <path_head_A_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_A_dx /2 width=2 by/
+  | <path_head_S_dx #Hq
+    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
+    <lift_rmap_S_dx /2 width=2 by/
   ]
 ]
 qed-.
 
-lemma tls_lift_rmap_append_closed (f) (p) (q) (n):
-      qᴿ = ↳[n](p●q)ᴿ →
-      ↑[p]f ≗ ⇂*[n]↑[p●q]f.
-#f #p #q #n #H0
->(reverse_reverse p) >(reverse_reverse q)
-/2 width=1 by tls_plus_lift_rmap_reverse_closed/
+lemma tls_lift_rmap_closed (f) (q) (n):
+      q = ↳[n]q →
+      f ≗ ⇂*[n]↑[q]f.
+#f #q #n #H0
+/2 width=1 by tls_plus_lift_rmap_closed/
 qed.