update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / ibfr_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_constructors.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/reduction/ibfr.ma".
+include "delayed_updating/substitution/fsubst_constructors.ma".
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/syntax/prototerm_constructors_eq.ma".
+
+(* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
+
+(* Constructions with constructors for prototerm ****************************)
+
+lemma ibfr_abst_hd (t1) (t2) (r):
+      t1 ➡𝐢𝐛𝐟[r] t2 → 𝛌.t1 ➡𝐢𝐛𝐟[𝗟◗r] 𝛌.t2.
+#t1 #t2 #r *
+#p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex6_5_intro … (𝗟◗p) … Hb Hm Hn) -Hb -Hm -Hn
+[ -Ht2 //
+| -Ht2 /2 width=1 by in_comp_abst_hd/
+| @(subset_eq_trans … (abst_eq_repl … Ht2)) -Ht1 -Ht2
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @fsubst_eq_repl // @lift_term_eq_repl_dx
+  >list_cons_shift @(subset_eq_canc_sn … (grafted_abst_hd … )) //
+]
+qed.
+
+lemma ibfr_appl_hd (v) (t1) (t2) (r):
+      t1 ➡𝐢𝐛𝐟[r] t2 → ＠v.t1 ➡𝐢𝐛𝐟[𝗔◗r] ＠v.t2.
+#v #t1 #t2 #r *
+#p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex6_5_intro … (𝗔◗p) … Hb Hm Hn) -Hb -Hm -Hn
+[ -Ht2 //
+| -Ht2 /2 width=1 by in_comp_appl_hd/
+| @(subset_eq_trans … (appl_eq_repl … Ht2)) -Ht1 -Ht2 [|*: // ]
+  @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @fsubst_eq_repl // @lift_term_eq_repl_dx
+  >list_cons_shift @(subset_eq_canc_sn … (grafted_appl_hd … )) //
+]
+qed.
+
+lemma ibfr_appl_sd (v1) (v2) (t) (r):
+      v1 ➡𝐢𝐛𝐟[r] v2 → ＠v1.t ➡𝐢𝐛𝐟[𝗦◗r] ＠v2.t.
+#v1 #v2 #t #r *
+#p #b #q #m #n #Hr #Hb #Hm #Hn #Hv1 #Hv2 destruct
+@(ex6_5_intro … (𝗦◗p) … Hb Hm Hn) -Hb -Hm -Hn
+[ -Hv2 //
+| -Hv2 /2 width=1 by in_comp_appl_sd/
+| @(subset_eq_trans ????? (appl_eq_repl …)) [3: @Hv2 |2,4: // |5: skip ]
+  @(subset_eq_canc_sn … (fsubst_appl_sd …)) @appl_eq_repl [| // ]
+  @fsubst_eq_repl // @lift_term_eq_repl_dx
+  >list_cons_shift @(subset_eq_canc_sn … (grafted_appl_sd … )) //
+]
+qed.
+
+lemma ibfr_beta_0 (v) (t) (q) (n):
+      q ϵ 𝐂❨Ⓕ,n❩ → q◖𝗱↑n ϵ t →
+      ＠v.𝛌.t ➡𝐢𝐛𝐟[𝗔◗𝗟◗q] ＠v.𝛌.(t[⋔q←🠡[𝐮❨↑n❩]v]).
+#v #t #q #n #Hn #Ht
+@(ex6_5_intro … (𝐞) (𝐞) q (𝟎) … Hn) -Hn
+[ //
+| //
+| //
+| /3 width=1 by in_comp_appl_hd, in_comp_abst_hd/
+| @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @fsubst_eq_repl // <nplus_zero_sn @lift_term_eq_repl_dx
+  >list_cons_comm @(subset_eq_canc_sn … (grafted_appl_sd … ))
+  @(subset_eq_canc_sn … (grafted_empty_dx … )) //
+]
+qed.
+
+lemma ibfr_beta_1 (v) (v1) (t) (q) (n):
+      q ϵ 𝐂❨Ⓕ,n❩ → q◖𝗱↑n ϵ t →
+      ＠v.＠v1.𝛌.𝛌.t ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝗟◗q] ＠v.＠v1.𝛌.𝛌.(t[⋔q←🠡[𝐮❨↑↑n❩]v]).
+#v #v1 #t #q #n #Hn #Ht
+@(ex6_5_intro … (𝐞) (𝗔◗𝗟◗𝐞) q (𝟏) … Hn) -Hn
+[ //
+| /2 width=1 by pbc_empty, pbc_redex/
+| /3 width=1 by pcc_A_sn, pcc_L_sn, pcc_empty/
+| /5 width=1 by in_comp_appl_hd, in_comp_abst_hd/
+| @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @(subset_eq_canc_sn … (fsubst_appl_hd …)) @appl_eq_repl [ // ]
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @(subset_eq_canc_sn … (fsubst_abst_hd …)) @abst_eq_repl
+  @fsubst_eq_repl // <nplus_unit_sn @lift_term_eq_repl_dx
+  >list_cons_comm @(subset_eq_canc_sn … (grafted_appl_sd … ))
+  @(subset_eq_canc_sn … (grafted_empty_dx … )) //
+]
+qed.