update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
index 772cc8d09ea3921aaaff0fe0a6ada18700f96751..6bbffaa7704293f6363ab6e139cd32a3209d3f2f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
@@ -22,8 +22,8 @@ include "ground/relocation/xap.ma".
 (* Constructions with head for path *****************************************)
 
 lemma lift_path_head (f) (p) (q) (n):
-      pᴿ = ↳[n](pᴿ●qᴿ) →
-      ↳[↑[q●p]f＠❨n❩](↑[f](q●p))ᴿ = (↑[↑[q]f]p)ᴿ.
+      pᴿ = ↳[n](pᴿ) →
+      ↳[↑[q●p]f＠❨n❩](↑[↑[q]f]p)ᴿ = (↑[↑[q]f]p)ᴿ.
 #f #p @(list_ind_rcons … p) -p
 [ #q #n #H0
   <(eq_inv_path_empty_head … H0) -H0
@@ -34,33 +34,28 @@ lemma lift_path_head (f) (p) (q) (n):
     [ <reverse_rcons <path_head_d_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_d_dx <lift_path_d_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_d_sn >tr_xap_succ_nap
-      <lift_path_d_dx >lift_rmap_append <reverse_rcons
-      <(IH … H0) -IH -H0 <tr_xap_plus //
+      <tr_xap_succ_nap <path_head_d_sn
+      <(IH … H0) in ⊢ (???%); -IH -H0 <tr_xap_plus //
     | <reverse_rcons <path_head_m_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_m_dx <lift_path_m_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_m_sn >tr_xap_succ_nap
-      <lift_path_m_dx <reverse_rcons
-      <(IH … H0) -IH -H0 //
+      <tr_xap_succ_nap <path_head_m_sn
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
     | <reverse_rcons <path_head_L_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_L_dx <lift_path_L_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_L_sn >tr_xap_succ_nap
-      <lift_path_L_dx <reverse_rcons
-      <(IH … H0) -IH -H0 //
+      <tr_xap_succ_nap <path_head_L_sn
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
     | <reverse_rcons <path_head_A_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_A_dx <lift_path_A_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_A_sn >tr_xap_succ_nap
-      <lift_path_A_dx <reverse_rcons
-      <(IH … H0) -IH -H0 //
+      <tr_xap_succ_nap <path_head_A_sn
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
     | <reverse_rcons <path_head_S_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_S_dx <lift_path_S_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_S_sn >tr_xap_succ_nap
-      <lift_path_S_dx <reverse_rcons
-      <(IH … H0) -IH -H0 //
+      <tr_xap_succ_nap <path_head_S_sn
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
     ]
   ]
 ]