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
deleted file mode 100644 (file)
index ecf0eaf..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
+++ /dev/null
@@ -1,101 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "delayed_updating/unwind/unwind2_prototerm_eq.ma".
-include "delayed_updating/unwind/unwind2_path_append.ma".
-include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/syntax/preterm.ma".
-include "delayed_updating/syntax/prototerm_proper.ma".
-
-(* TAILED UNWIND FOR PRETERM ************************************************)
-
-(* Constructions with fsubst and pic ****************************************)
-
-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_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_ppc_dx /2 width=3 by ppc_rcons/ ]
-  ]
-]
-qed-.
-
-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_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/ ] *
-  [ <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_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_ppc_sn, conj, unwind2_term_fsubst_ppc_dx/ qed.