update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind2 / unwind_fsubst.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma
new file mode 100644 (file)
index 0000000..fedc665
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unwind2/unwind_prototerm_eq.ma".
+include "delayed_updating/unwind2/unwind_structure.ma".
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/preterm.ma".
+include "delayed_updating/syntax/prototerm_proper.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with fsubst ************************************************)
+
+lemma unwind_fsubst_sn (f) (t) (u) (p): u ϵ 𝐏 →
+      (▼[f]t)[⋔(⊗p)←▼[▼[p]f]u] ⊆ ▼[f](t[⋔p←u]).
+#f #t #u #p #Hu #ql * *
+[ #rl * #r #Hr #H1 #H2 destruct
+  >unwind_append_proper_dx
+  /4 width=5 by in_comp_unwind_bi, in_ppc_comp_trans, or_introl, ex2_intro/
+| * #q #Hq #H1 #H0
+  @(ex2_intro … H1) @or_intror @conj // *
+  [ <list_append_empty_dx #H2 destruct
+    elim (unwind_path_root f q) #r #_ #Hr /2 width=2 by/
+  | #l #r #H2 destruct
+    @H0 -H0 [| <unwind_append_proper_dx /2 width=3 by ppc_lcons/ ]
+  ]
+]
+qed-.
+
+lemma unwind_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
+      ▼[f](t[⋔p←u]) ⊆ (▼[f]t)[⋔(⊗p)←▼[▼[p]f]u].
+#f #t #u #p #Hu #H1p #H2p #ql * #q * *
+[ #r #Hu #H1 #H2 destruct
+  @or_introl @ex2_intro
+  [|| <unwind_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
+  /2 width=3 by ex2_intro/
+| #Hq #H0 #H1 destruct
+  @or_intror @conj [ /2 width=1 by in_comp_unwind_bi/ ] *
+  [ <list_append_empty_dx #Hr @(H0 … (𝐞)) -H0
+    <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
+  | #l #r #Hr
+    elim (unwind_inv_append_proper_dx … Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
+    lapply (H2p … Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
+  ]
+]
+qed-.
+
+lemma unwind_fsubst (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 𝐓 →
+      (▼[f]t)[⋔(⊗p)←▼[▼[p]f]u] ⇔ ▼[f](t[⋔p←u]).
+/4 width=3 by unwind_fsubst_sn, conj, unwind_fsubst_dx/ qed.