update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_rmap_crux.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_crux.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_crux.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_crux.ma
@@ -0,0 +1,43 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_k/unwind2_rmap_closed.ma".
+
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
+
+(* Crucial constructions with tr_uni ****************************************)
+
+(* Note: crux of the commutation between unwind and balanced focused reduction *)
+lemma unwind2_rmap_uni_crux (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨Ⓕ,m,𝟎❩ → q ϵ 𝐂❨Ⓕ,n,𝟎❩ →
+      (𝐮❨↑(♭b+♭q)❩ ∘ ▶[f]p ≗ ▶[f](p●𝗔◗b●𝗟◗q) ∘ 𝐮❨↑(m+n)❩).
+#f #p #b #q #m #n #Hm #Hn
+<list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
+>list_append_rcons_sn >(list_append_rcons_sn … b)
+@(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
+@(stream_eq_trans ????? (tr_compose_eq_repl …))
+[| @tls_succ_plus_unwind2_rmap_append_closed_Lq_dx // | skip
+|  <nap_plus_unwind2_rmap_append_closed_Lq_dx // | skip
+] -Hn
+@tr_eq_inv_nap_zero_tl_bi
+[ <tr_compose_nap <tr_compose_nap <tr_uni_nap <tr_uni_nap
+  >nsucc_unfold >nplus_succ_dx >nplus_succ_dx <nplus_assoc <nplus_assoc
+  >tr_nap_plus_dx <unwind2_rmap_append <nap_plus_unwind2_rmap_closed
+  /2 width=4 by pcc_A_sn/
+| @(stream_eq_canc_sn … (tr_tl_compose_uni_sn …))
+  @(stream_eq_trans ????? (tr_tl_compose_uni_sn …))
+  >stream_tls_succ <unwind2_rmap_append
+  /3 width=2 by tls_succ_unwind2_rmap_closed, pcc_A_sn/
+]
+qed-.