partial update in delayed_updating

+ WIP

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 25d728a89772898100b6bb8e3dfe0d256eabb7a9..9a3584bb96e05761f519ef09a105bf8fafe2d7cb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -19,15 +19,55 @@ include "delayed_updating/substitution/fsubst_eq.ma".
 include "delayed_updating/substitution/lift_constructors.ma".
 include "delayed_updating/substitution/lift_preterm_eq.ma".
 include "delayed_updating/substitution/lift_structure_depth.ma".
+include "delayed_updating/substitution/lift_depth.ma".
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
 include "ground/relocation/tr_uni_compose.ma".
 include "ground/relocation/tr_pap_pushs.ma".
 
-include "ground/lib/stream_eq_eq.ma".
-
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
+lemma tr_uni_eq_repl (n1) (n2):
+      n1 = n2 → 𝐮❨n1❩ ≗ 𝐮❨n2❩.
+// qed.
+
+axiom pippo (b) (q) (n):
+      ↑❘q❘ = (↑[q]𝐢)@❨n❩ →
+      ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
+
+lemma lift_rmap_tls_eq_id (p) (n):
+      ❘p❘ = ↑[p]𝐢@❨n❩ →
+      (𝐢) ≗ ⇂*[n]↑[p]𝐢.
+#p @(list_ind_rcons … p) -p
+[ #n <depth_empty #H destruct
+| #p * [ #m ] #IH #n
+  [ <depth_d_dx <lift_rmap_pap_d_dx #H0
+    @(stream_eq_trans … (lift_rmap_tls_d_dx …))
+    @(stream_eq_trans … (IH …)) -IH //
+  | /2 width=1 by/
+  | <depth_L_dx <lift_rmap_L_dx
+    cases n -n [| #n ] #H0
+    [
+    | 
+    ]
+  | /2 width=1 by/
+  | /2 width=1 by/
+  ]
+]
+
+
+(*  (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
+(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
+lemma lift_rmap_tls_eq (f) (p) (n):
+      ❘p❘ = ↑[p]𝐢@❨n❩ →
+      f ≗ ⇂*[n]↑[p]f.
+#f #p #n #Hp
+@(stream_eq_canc_dx … (stream_tls_eq_repl …))
+[| @lift_rmap_decompose | skip ]
+<tr_compose_tls <Hp
+
+@(stream_eq_canc_dx) … (lift_rmap_decompose …)) 
+
 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
       t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
 #f #p #q #t1 #t2 #H0t1
@@ -41,7 +81,7 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
 | lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (lift_fsubst …))
-  [ <lift_rmap_append <lift_rmap_A_sn <lift_rmap_append <lift_rmap_L_sn
+  [ <lift_rmap_append <lift_rmap_A_sn (* <lift_rmap_append <lift_rmap_L_sn *)
     <structure_append <structure_A_sn <structure_append <structure_L_sn
     <depth_append <depth_L_sn <depth_structure <depth_structure
     @fsubst_eq_repl [ // ]
@@ -52,10 +92,13 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
     @(subset_eq_canc_dx … (lift_term_after …))
     @lift_term_eq_repl_sn -t1
     @(stream_eq_trans … (tr_compose_uni_dx …))
+    lapply (Hn (𝐢)) -Hn >tr_id_unfold #Hn
+    lapply (pippo … b … Hn) -Hn #Hn
     @tr_compose_eq_repl
-(*    
-    >nrplus_inj_dx <tr_pap_plus
-*)    
+    [ <lift_rmap_pap_le //
+      <Hn <nrplus_inj_sn //
+    |
+    ]
   | //
   | /2 width=2 by ex_intro/
   | //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
index cefb45d49c977fd1f4fb7989ebc9fd32fd64a8fa..bf6831e80356072b6397c902a13803ee6610d791 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
@@ -39,3 +39,10 @@ lemma lift_rmap_decompose (p) (f):
   ]
 ]
 qed.
+
+lemma lift_rmap_pap_le (f) (p) (n):
+      (↑[p]𝐢)@❨n❩ < ↑❘p❘ → (↑[p]𝐢)@❨n❩ = (↑[p]f)@❨n❩.
+#f #p #n #Hn
+>(tr_pap_eq_repl … (↑[p]f) … (lift_rmap_decompose …))
+<tr_compose_pap @tr_pap_pushs_le //
+qed.