update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dfr_ifr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index be7f3b3d3d3825973ccb0af6aa5360a0cbb7b7a2..e54dd267877972e510e4b7d12516e0506efe9654 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -18,9 +18,11 @@ include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/unwind/unwind2_constructors.ma".
 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
+include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
 include "delayed_updating/unwind/unwind2_rmap_head.ma".
 
 include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
 
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
 include "delayed_updating/syntax/path_head_structure.ma".
@@ -33,7 +35,7 @@ include "delayed_updating/syntax/path_depth_reverse.ma".
 (* Main destructions with ifr ***********************************************)
 
 theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
-        t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
+        t1 â\9e¡ð\9d\90\9dð\9d\90\9f[p,q] t2 â\86\92 â\96¼[f]t1 â\9e¡ð\9d\90¢ð\9d\90\9f[â\8a\97p,â\8a\97q] â\96¼[f]t2.
 #f #p #q #t1 #t2 #H0t1
 * #n * #H1n #Ht1 #Ht2
 @(ex_intro … (↑♭q)) @and3_intro
@@ -51,19 +53,18 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
   @(subset_eq_trans … (unwind2_term_fsubst …))
   [ @fsubst_eq_repl [ // | // ]
     @(subset_eq_trans … (unwind2_term_iref …))
-    @(subset_eq_canc_sn … (unwind2_term_eq_repl_dx …))
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
     [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
-    @(subset_eq_trans … (unwind2_term_after …))
+    @(subset_eq_trans … (lift_unwind2_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    @nstream_eq_inv_ext #m
-    <tr_compose_pap <tr_compose_pap
-    <tr_uni_pap <tr_uni_pap <tr_pap_plus
     >list_append_rcons_sn in H1n; <reverse_append #H1n
-    lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
-    >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
-    <(tr_pap_eq_repl … H2n) -H2n //
+    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_sn <reverse_rcons
+      /2 width=1 by tls_unwind2_rmap_append_closed/
+    ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/