update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind / unwind2_preterm_fsubst.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
index 19634dccc1b2a0866c00e12a9194af04738525b4..ecf0eaf0f7d1b131fd80decb6a63ebc9fb39c545 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
@@ -20,30 +20,69 @@ include "delayed_updating/syntax/prototerm_proper.ma".
 
 (* TAILED UNWIND FOR PRETERM ************************************************)
 
-(* Constructions with fsubst ************************************************)
+(* Constructions with fsubst and pic ****************************************)
 
-lemma unwind2_term_fsubst_sn (f) (t) (u) (p): u ϵ 𝐏 →
+lemma unwind2_term_fsubst_pic_sn (f) (t) (u) (p): p ϵ 𝐈 →
+      (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u] ⊆ ▼[f](t[⋔p←u]).
+#f #t #u #p #Hp #ql * *
+[ #rl * #r #Hr #H1 #H2 destruct
+  >unwind2_path_append_pic_sn
+  /4 width=3 by in_comp_unwind2_path_term, or_introl, ex2_intro/
+| * #q #Hq #H1 #H0
+  @(ex2_intro … H1) @or_intror @conj // *
+  [ <list_append_empty_sn #H2 destruct
+    elim (unwind2_path_root f q) #r #_ #Hr /2 width=2 by/
+  | #l #r #H2 destruct
+    /3 width=2 by unwind2_path_append_pic_sn/
+  ]
+]
+qed-.
+
+lemma unwind2_term_fsubst_pic_dx (f) (t) (u) (p): p ϵ 𝐈 → p ϵ ▵t → t ϵ 𝐓 →
+      ▼[f](t[⋔p←u]) ⊆ (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u].
+#f #t #u #p #Hp #H1p #H2p #ql * #q * *
+[ #r #Hu #H1 #H2 destruct
+  /5 width=3 by unwind2_path_append_pic_sn, ex2_intro, or_introl/
+| #Hq #H0 #H1 destruct
+  @or_intror @conj [ /2 width=1 by in_comp_unwind2_path_term/ ] *
+  [ <list_append_empty_sn #Hr @(H0 … (𝐞)) -H0
+    <list_append_empty_sn @H2p -H2p
+    /2 width=2 by unwind2_path_des_structure, prototerm_in_comp_root/
+  | #l #r #Hr
+    elim (unwind2_path_inv_append_ppc_dx … Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
+    lapply (H2p … Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
+  ]
+]
+qed-.
+
+lemma unwind2_term_fsubst_pic (f) (t) (u) (p): p ϵ 𝐈 → p ϵ ▵t → t ϵ 𝐓 →
+      (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u] ⇔ ▼[f](t[⋔p←u]).
+/4 width=3 by unwind2_term_fsubst_pic_sn, conj, unwind2_term_fsubst_pic_dx/ qed.
+
+(* Constructions with fsubst and ppc ****************************************)
+
+lemma unwind2_term_fsubst_ppc_sn (f) (t) (u) (p): u ϵ 𝐏 →
       (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u] ⊆ ▼[f](t[⋔p←u]).
 #f #t #u #p #Hu #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
-  >unwind2_path_append_proper_dx
+  >unwind2_path_append_ppc_dx
   /4 width=5 by in_comp_unwind2_path_term, in_comp_tpc_trans, or_introl, ex2_intro/
 | * #q #Hq #H1 #H0
   @(ex2_intro … H1) @or_intror @conj // *
   [ <list_append_empty_sn #H2 destruct
     elim (unwind2_path_root f q) #r #_ #Hr /2 width=2 by/
   | #l #r #H2 destruct
-    @H0 -H0 [| <unwind2_path_append_proper_dx /2 width=3 by ppc_rcons/ ]
+    @H0 -H0 [| <unwind2_path_append_ppc_dx /2 width=3 by ppc_rcons/ ]
   ]
 ]
 qed-.
 
-lemma unwind2_term_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
+lemma unwind2_term_fsubst_ppc_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       ▼[f](t[⋔p←u]) ⊆ (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u].
 #f #t #u #p #Hu #H1p #H2p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
-  [|| <unwind2_path_append_proper_dx /2 width=5 by in_comp_tpc_trans/ ]
+  [|| <unwind2_path_append_ppc_dx /2 width=5 by in_comp_tpc_trans/ ]
   /2 width=3 by ex2_intro/
 | #Hq #H0 #H1 destruct
   @or_intror @conj [ /2 width=1 by in_comp_unwind2_path_term/ ] *
@@ -51,12 +90,12 @@ lemma unwind2_term_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 
     <list_append_empty_sn @H2p -H2p
     /2 width=2 by unwind2_path_des_structure, prototerm_in_comp_root/
   | #l #r #Hr
-    elim (unwind2_path_inv_append_proper_dx … Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
+    elim (unwind2_path_inv_append_ppc_dx … Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
     lapply (H2p … Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
   ]
 ]
 qed-.
 
-lemma unwind2_term_fsubst (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
+lemma unwind2_term_fsubst_ppc (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
       (▼[f]t)[⋔(⊗p)←▼[▶[f]p]u] ⇔ ▼[f](t[⋔p←u]).
-/4 width=3 by unwind2_term_fsubst_sn, conj, unwind2_term_fsubst_dx/ qed.
+/4 width=3 by unwind2_term_fsubst_ppc_sn, conj, unwind2_term_fsubst_ppc_dx/ qed.