update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected.ma
index 7c92760210cf1efaf2e1bb7edf61ba51e3870519..753d38c684100ddfd25a544e61283d4dceb6dfb4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected.ma
@@ -12,32 +12,33 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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 ***************************************)
 
-(* Prerequisites ************************************************************)
+(* Example of unprotected balanced β-reduction ******************************)
 
-lemma list_rcons_prop_1 (A) (a1) (a2):
-      ⓔ ⨭ a1 ⨭{A} a2 = a1 ⨮ (ⓔ ⨭ a2).
-// qed.
+definition l3_t: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.⧣𝟏).
 
-(* Example of unprotected balanced β-reduction ******************************)
+definition l3_i1: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣𝟏).
 
-definition l3_t0: prototerm ≝
-           (𝛌.＠(⧣𝟏).＠(𝛌.＠(⧣𝟐).⧣𝟏).𝛌.⧣𝟏).
+definition l3_i2: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣↑𝟐).
 
-definition l3_t1: prototerm ≝
-           (𝛌.＠(⧣𝟏).＠(𝛌.＠(⧣𝟐).⧣𝟏).𝛌.(𝛌.＠(⧣↑𝟐).⧣𝟏)).
+definition l3_d1: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.⧣𝟏).
 
-definition l3_t2: prototerm ≝
-           (𝛌.＠(⧣𝟏).＠(𝛌.＠(⧣𝟐).⧣𝟏).𝛌.(𝛌.＠(⧣↑𝟐).⧣↑𝟐)).
+definition l3_d2: prototerm ≝
+           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.𝛕𝟏.⧣𝟏).
 
-lemma l3_t01:
-      l3_t0 ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗔◗𝗟◗𝐞] l3_t1.
-@ibfr_abst_hd
+lemma l3_ti1:
+      l3_t ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝐞] l3_i1.
 @ibfr_appl_hd
 @ibfr_eq_trans [| @ibfr_beta_0 // ]
 @appl_eq_repl [ // ]
@@ -45,24 +46,40 @@ lemma l3_t01:
 @(subset_eq_canc_sn … (fsubst_empty_rc …))
 @(subset_eq_canc_sn … (lift_term_abst …))
 @abst_eq_repl
-@(subset_eq_canc_sn … (lift_term_appl … ))
-@appl_eq_repl
 @(subset_eq_canc_sn … (lift_term_oref_pap … )) //
 qed.
 
-lemma l3_t12:
-      l3_t1 ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗔◗𝗟◗𝗟◗𝗔◗𝐞] l3_t2.
-@ibfr_abst_hd
-@ibfr_eq_trans
-[| @(ibfr_beta_1 … (𝟎)) [| <list_rcons_prop_1 ]
-   /2 width=3 by pcc_A_sn, in_comp_appl_hd/
-]
+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_appl_hd …))
-@appl_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.