+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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 ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).⧣𝟏).
-
-definition l3_i1: prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛌.⧣𝟏).
-
-definition l3_i2: prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛌.⧣↑𝟐).
-
-definition l3_i2': prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛌.⧣↑↑𝟐).
-
-definition l3_d1: prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛕𝟏.(𝛌.⧣𝟏)).
-
-definition l3_d2: prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛕𝟏.𝛌.(⧣𝟐)).
-
-definition l3_d2': prototerm ≝
- (𝛌.@(𝛌.⧣𝟏).𝛌.@(⧣𝟐).𝛕𝟏.𝛌.𝛕𝟏.(⧣𝟐)).
-
-lemma l3_ti1:
- l3_t ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_i1.
-@ibfr_abst_hd
-@ibfr_eq_trans
-[ | @(ibfr_beta_0 … (𝟎))
- [ /2 width=1 by pcc_A_sn, pcc_empty/
- | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
- ]
-]
-@appl_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_abst …))
-@abst_eq_repl
-@(subset_eq_canc_sn … (lift_term_oref_pap … )) //
-qed.
-
-lemma l3_i12:
- l3_i1 ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝗟◗𝐞] l3_i2.
-@ibfr_abst_hd
-@ibfr_appl_hd
-@ibfr_abst_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_oref_pap … )) //
-qed.
-
-lemma l3_td1:
- l3_t ➡𝐝𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_d1.
-@dbfr_abst_hd
-@dbfr_eq_trans
-[ | @(dbfr_beta_0 … (𝟎))
- [ /2 width=1 by pcc_A_sn, pcc_empty/
- | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
- ]
-]
-@appl_eq_repl [ // ]
-@abst_eq_repl
-@(subset_eq_canc_sn … (fsubst_appl_hd …))
-@appl_eq_repl [ // ]
-@(subset_eq_canc_sn … (fsubst_empty_rc …))
-@iref_eq_repl //
-qed.
-
-lemma l3_di2:
- l3_i2 ⇔ ▼[𝐢]l3_d2.
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(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_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(subset_eq_canc_sn … (unwind2_term_iref …))
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-qed.
-
-lemma l3_di2':
- l3_i2' ⇔ ▼[𝐢]l3_d2'.
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(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_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(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.