partial 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 66209d837bd869cca939b8b7e94ec01075614950..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
@@ -12,49 +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) (n) (k):
+lemma tls_plus_lift_rmap_closed (f) (q) (n) (m):
       q = ↳[n]q →
-      ⇂*[k]f ≗ ⇂*[n+k]↑[qᴿ]f.
+      ⇂*[m]f ≗ ⇂*[n+m]↑[q]f.
 #f #q elim q -q
-[ #n #k #Hq
+[ #n #m #Hq
   <(eq_inv_path_empty_head … Hq) -n //
 | #l #q #IH #n @(nat_ind_succ … n) -n //
-  #n #_ #k cases l [ #m ]
-  [ <path_head_d_sn #Hq
-    elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hp <nrplus_inj_sn
-    <reverse_lcons
+  #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 #Hq
+  | <path_head_m_dx #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-    <reverse_lcons <lift_rmap_m_dx /2 width=1 by/
-  | <path_head_L_sn #Hq
+    <lift_rmap_m_dx /2 width=1 by/
+  | <path_head_L_dx #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-    <reverse_lcons <lift_rmap_L_dx <nplus_succ_sn /2 width=1 by/
-  | <path_head_A_sn #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
-    <reverse_lcons <lift_rmap_A_dx /2 width=2 by/
-  | <path_head_S_sn #Hq
+    <lift_rmap_A_dx /2 width=2 by/
+  | <path_head_S_dx #Hq
     elim (eq_inv_list_lcons_bi ????? Hq) -Hq #_ #Hq
-    <reverse_lcons <lift_rmap_S_dx /2 width=2 by/
+    <lift_rmap_S_dx /2 width=2 by/
   ]
 ]
 qed-.
 
 lemma tls_lift_rmap_closed (f) (q) (n):
-      qᴿ = ↳[n](qᴿ) →
+      q = ↳[n]q →
       f ≗ ⇂*[n]↑[q]f.
 #f #q #n #H0
->(reverse_reverse q)
-/2 width=1 by tls_plus_lift_rmap_reverse_closed/
+/2 width=1 by tls_plus_lift_rmap_closed/
 qed.