+++ /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/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 ā”š¢šš[r] t2 ā š.t1 ā”š¢šš[šār] š.t2.
-#t1 #t2 #r *
-#p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
-@(ex6_5_intro ā¦ (šāp) ā¦ Hb Hm Hn) -Hb -Hm -Hn
-[ -Ht2 //
-| -Ht2 /2 width=1 by in_comp_abst_hd/
-| @(subset_eq_trans ā¦ (abst_eq_repl ā¦ Ht2)) -Ht1 -Ht2
- @(subset_eq_canc_sn ā¦ (fsubst_abst_hd ā¦)) @abst_eq_repl
- @fsubst_eq_repl // @lift_term_eq_repl_dx
- >list_cons_shift @(subset_eq_canc_sn ā¦ (grafted_abst_hd ā¦ )) //
-]
-qed.
-
-lemma ibfr_appl_hd (v) (t1) (t2) (r):
- t1 ā”š¢šš[r] t2 ā ļ¼ v.t1 ā”š¢šš[šār] ļ¼ v.t2.
-#v #t1 #t2 #r *
-#p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
-@(ex6_5_intro ā¦ (šāp) ā¦ Hb Hm Hn) -Hb -Hm -Hn
-[ -Ht2 //
-| -Ht2 /2 width=1 by in_comp_appl_hd/
-| @(subset_eq_trans ā¦ (appl_eq_repl ā¦ Ht2)) -Ht1 -Ht2 [|*: // ]
- @(subset_eq_canc_sn ā¦ (fsubst_appl_hd ā¦)) @appl_eq_repl [ // ]
- @fsubst_eq_repl // @lift_term_eq_repl_dx
- >list_cons_shift @(subset_eq_canc_sn ā¦ (grafted_appl_hd ā¦ )) //
-]
-qed.
-
-lemma ibfr_appl_sd (v1) (v2) (t) (r):
- v1 ā”š¢šš[r] v2 ā ļ¼ v1.t ā”š¢šš[š¦ār] ļ¼ v2.t.
-#v1 #v2 #t #r *
-#p #b #q #m #n #Hr #Hb #Hm #Hn #Hv1 #Hv2 destruct
-@(ex6_5_intro ā¦ (š¦āp) ā¦ Hb Hm Hn) -Hb -Hm -Hn
-[ -Hv2 //
-| -Hv2 /2 width=1 by in_comp_appl_sd/
-| @(subset_eq_trans ????? (appl_eq_repl ā¦)) [3: @Hv2 |2,4: // |5: skip ]
- @(subset_eq_canc_sn ā¦ (fsubst_appl_sd ā¦)) @appl_eq_repl [| // ]
- @fsubst_eq_repl // @lift_term_eq_repl_dx
- >list_cons_shift @(subset_eq_canc_sn ā¦ (grafted_appl_sd ā¦ )) //
-]
-qed.
-
-lemma ibfr_beta_0 (v) (t) (q) (n):
- q Ļµ šāØā»,nā© ā qāš±ān Ļµ t ā
- ļ¼ v.š.t ā”š¢šš[šāšāq] ļ¼ v.š.(t[āqāš ”[š®āØānā©]v]).
-#v #t #q #n #Hn #Ht
-@(ex6_5_intro ā¦ (š) (š) q (š) ā¦ Hn) -Hn
-[ //
-| //
-| //
-| /3 width=1 by in_comp_appl_hd, in_comp_abst_hd/
-| @(subset_eq_canc_sn ā¦ (fsubst_appl_hd ā¦)) @appl_eq_repl [ // ]
- @(subset_eq_canc_sn ā¦ (fsubst_abst_hd ā¦)) @abst_eq_repl
- @fsubst_eq_repl // <nplus_zero_sn @lift_term_eq_repl_dx
- >list_cons_comm @(subset_eq_canc_sn ā¦ (grafted_appl_sd ā¦ ))
- @(subset_eq_canc_sn ā¦ (grafted_empty_dx ā¦ )) //
-]
-qed.
-
-lemma ibfr_beta_1 (v) (v1) (t) (q) (n):
- q Ļµ šāØā»,nā© ā qāš±ān Ļµ t ā
- ļ¼ v.ļ¼ v1.š.š.t ā”š¢šš[šāšāšāšāq] ļ¼ v.ļ¼ v1.š.š.(t[āqāš ”[š®āØāānā©]v]).
-#v #v1 #t #q #n #Hn #Ht
-@(ex6_5_intro ā¦ (š) (šāšāš) q (š) ā¦ 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 ā¦ (fsubst_appl_hd ā¦)) @appl_eq_repl [ // ]
- @(subset_eq_canc_sn ā¦ (fsubst_appl_hd ā¦)) @appl_eq_repl [ // ]
- @(subset_eq_canc_sn ā¦ (fsubst_abst_hd ā¦)) @abst_eq_repl
- @(subset_eq_canc_sn ā¦ (fsubst_abst_hd ā¦)) @abst_eq_repl
- @fsubst_eq_repl // <nplus_unit_sn @lift_term_eq_repl_dx
- >list_cons_comm @(subset_eq_canc_sn ā¦ (grafted_appl_sd ā¦ ))
- @(subset_eq_canc_sn ā¦ (grafted_empty_dx ā¦ )) //
-]
-qed.