update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / reduction / dbfr_unprotected.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc
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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/dbfr_constructors.ma".
+include "delayed_updating/reduction/ibfr_constructors.ma".
+include "delayed_updating/unwind/unwind2_prototerm_constructors.ma".
+include "delayed_updating/substitution/lift_prototerm_constructors.ma".
+include "ground/arith/pnat_two.ma".
+
+(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
+
+(* Example of unprotected balanced β-reduction ******************************)
+
+definition l3_t: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.⧣𝟏).
+
+definition l3_i1: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣𝟏).
+
+definition l3_i2: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣↑𝟐).
+
+definition l3_d1: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.⧣𝟏).
+
+definition l3_d2: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.𝛕𝟏.⧣𝟏).
+
+lemma l3_ti1:
+      l3_t ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝐞] l3_i1.
+@ibfr_appl_hd
+@ibfr_eq_trans [| @ibfr_beta_0 // ]
+@appl_eq_repl [ // ]
+@abst_eq_repl
+@(subset_eq_canc_sn … (fsubst_empty_rc …))
+@(subset_eq_canc_sn … (lift_term_abst …))
+@abst_eq_repl
+@(subset_eq_canc_sn … (lift_term_oref_pap … )) //
+qed.
+
+lemma l3_i12:
+      l3_i1 ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝗟◗𝐞] l3_i2.
+@ibfr_eq_trans [| @ibfr_beta_1 // ]
+@appl_eq_repl [ // ]
+@appl_eq_repl [ // ]
+@abst_eq_repl
+@abst_eq_repl
+@(subset_eq_canc_sn … (fsubst_empty_rc …))
+@(subset_eq_canc_sn … (lift_term_oref_pap … )) //
+qed.
+
+lemma l3_td1:
+      l3_t ➡𝐝𝐛𝐟[𝗔◗𝗔◗𝗟◗𝐞] l3_d1.
+@dbfr_appl_hd
+@dbfr_eq_trans [| @dbfr_beta_0 // ]
+@appl_eq_repl [ // ]
+@abst_eq_repl
+@(subset_eq_canc_sn … (fsubst_empty_rc …)) //
+qed.
+
+lemma ld_di2:
+      l3_i2 ⇔ ▼[𝐢]l3_d2.
+@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
+[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) // ]
+@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
+[ @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+  @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+]
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+@(subset_eq_canc_sn … (unwind2_term_iref …))
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+@(subset_eq_canc_sn … (unwind2_term_iref …))
+@(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+qed.