-(**************************************************************************)
-(* ___ *)
-(* ||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/dfr.ma".
-include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/substitution/fsubst_unwind.ma".
-include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/unwind_constructors.ma".
-include "delayed_updating/substitution/unwind_preterm_eq.ma".
-include "delayed_updating/substitution/unwind_structure_depth.ma".
-include "delayed_updating/substitution/unwind_depth.ma".
-include "delayed_updating/syntax/prototerm_proper_constructors.ma".
-include "delayed_updating/syntax/path_structure_depth.ma".
-include "ground/relocation/tr_uni_compose.ma".
-include "ground/relocation/tr_pap_pushs.ma".
-
-(* DELAYED FOCUSED REDUCTION ************************************************)
-
-lemma tr_uni_eq_repl (n1) (n2):
- n1 = n2 → 𝐮❨n1❩ ≗ 𝐮❨n2❩.
-// qed.
-
-axiom pippo (b) (q) (n):
- ↑❘q❘ = (↑[q]𝐢)@❨n❩ →
- ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
-
-lemma unwind_rmap_tls_eq_id (p) (n):
- ❘p❘ = ↑[p]𝐢@❨n❩ →
- (𝐢) ≗ ⇂*[n]↑[p]𝐢.
-#p @(list_ind_rcons … p) -p
-[ #n <depth_empty #H destruct
-| #p * [ #m ] #IH #n
- [ <depth_d_dx <unwind_rmap_pap_d_dx #H0
- @(stream_eq_trans … (unwind_rmap_tls_d_dx …))
- @(stream_eq_trans … (IH …)) -IH //
- | /2 width=1 by/
- | <depth_L_dx <unwind_rmap_L_dx
- cases n -n [| #n ] #H0
- [
- |
- ]
- | /2 width=1 by/
- | /2 width=1 by/
- ]
-]
-
-
-(* (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
-(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
-lemma unwind_rmap_tls_eq (f) (p) (n):
- ❘p❘ = ↑[p]𝐢@❨n❩ →
- f ≗ ⇂*[n]↑[p]f.
-#f #p #n #Hp
-@(stream_eq_canc_dx … (stream_tls_eq_repl …))
-[| @unwind_rmap_decompose | skip ]
-<tr_compose_tls <Hp
-
-@(stream_eq_canc_dx) … (unwind_rmap_decompose …))
-
-lemma dfr_unwind_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #b #n * #Hb #Hn #Ht1 #Ht2
-@(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
-[ //
-| #g <unwind_rmap_structure <depth_structure
- >tr_pushs_swap <tr_pap_pushs_le //
-| lapply (in_comp_unwind_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
- <unwind_path_d_empty_dx //
-| lapply (unwind_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
- @(subset_eq_trans … Ht2) -t2
- @(subset_eq_trans … (unwind_fsubst …))
- [ <unwind_rmap_append <unwind_rmap_A_sn (* <unwind_rmap_append <unwind_rmap_L_sn *)
- <structure_append <structure_A_sn <structure_append <structure_L_sn
- <depth_append <depth_L_sn <depth_structure <depth_structure
- @fsubst_eq_repl [ // ]
- @(subset_eq_trans … (unwind_iref …))
- @(subset_eq_canc_sn … (unwind_term_eq_repl_dx …))
- [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
- @(subset_eq_trans … (unwind_term_after …))
- @(subset_eq_canc_dx … (unwind_term_after …))
- @unwind_term_eq_repl_sn -t1
- @(stream_eq_trans … (tr_compose_uni_dx …))
- lapply (Hn (𝐢)) -Hn >tr_id_unfold #Hn
- lapply (pippo … b … Hn) -Hn #Hn
- @tr_compose_eq_repl
- [ <unwind_rmap_pap_le //
- <Hn <nrplus_inj_sn //
- |
- ]
- | //
- | /2 width=2 by ex_intro/
- | //
- ]
-]