From 9dd07546d24cfdcf62276ce4518a69e8bbf0f9d3 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Thu, 9 Nov 2017 21:59:39 +0000
Subject: [PATCH] advances on lfsx_csx ...

---
 .../basic_2/rt_computation/lfsx_csx.ma        | 37 +++++++++----------
 1 file changed, 18 insertions(+), 19 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma
index ff005164f..29ed16c91 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma
@@ -12,16 +12,20 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/rt_computation/lfpxs.ma".
 include "basic_2/rt_computation/csx_lsubr.ma".
+include "basic_2/rt_computation/lfsx_drops.ma".
 include "basic_2/rt_computation/lfsx_lfpxs.ma".
 
 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
-(*
+
 (* Advanced properties ******************************************************)
 
-lemma lsx_lref_be_lpxs: ∀h,o,I,G,K1,V,i,l. l ≤ yinj i → ⦃G, K1⦄ ⊢ ⬊*[h, o] V →
-                        ∀K2. G ⊢ ⬊*[h, o, V, 0] K2 → ⦃G, K1⦄ ⊢ ➡*[h, o] K2 →
-                        ∀L2. ⬇[i] L2 ≡ K2.ⓑ{I}V → G ⊢ ⬊*[h, o, #i, l] L2.
+(* Basic_2A1: uses: lsx_lref_be_lpxs *)
+axiom lfsx_pair_lpxs: ∀h,o,G,K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
+                      ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h, V] K2 →
+                      ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
+(*
 #h #o #I #G #K1 #V #i #l #Hli #H @(csx_ind_alt … H) -V
 #V0 #_ #IHV0 #K2 #H @(lsx_ind … H) -K2
 #K0 #HK0 #IHK0 #HK10 #L0 #HLK0 @lsx_intro
@@ -34,12 +38,14 @@ elim (eq_term_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnL02 -HLK0
   /3 width=4 by lsx_cpx_trans_O, lsx_lpx_trans, lpxs_cpx_trans, lpxs_strap1/ (**) (* full auto too slow *)
 ]
 qed.
-
-lemma lsx_lref_be: ∀h,o,I,G,K,V,i,l. l ≤ yinj i → ⦃G, K⦄ ⊢ ⬊*[h, o] V →
-                   G ⊢ ⬊*[h, o, V, 0] K →
-                   ∀L. ⬇[i] L ≡ K.ⓑ{I}V → G ⊢ ⬊*[h, o, #i, l] L.
-/2 width=8 by lsx_lref_be_lpxs/ qed.
 *)
+(* Basic_2A1: uses: lsx_lref_be *)
+lemma lfsx_lref_pair: ∀h,o,G,K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
+                      ∀I,L,i. ⬇*[i] L ≡ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
+#h #o #G #K #V #HV #HK #I #L #i #HLK
+@(lfsx_lifts … (#0) … HLK) -L /2 width=3 by lfsx_pair_lpxs/
+qed.
+
 (* Main properties **********************************************************)
 
 theorem csx_lsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
@@ -47,17 +53,10 @@ theorem csx_lsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ 
 #Z #Y #X #IH #G #L * * //
 [ #i #HG #HL #HT #H destruct
   elim (csx_inv_lref … H) -H [ |*: * ]
-  [ #HL
-  | #I #K #HLK
-  | #I #K #V #HLK #HV
+  [ /2 width=1 by lfsx_lref_atom/
+  | /2 width=3 by lfsx_lref_unit/
+  | /4 width=6 by lfsx_lref_pair, fqup_lref/
   ]
-(*
-  elim (lt_or_ge i (|L|)) /2 width=1 by lsx_lref_free/
-  elim (ylt_split i l) /2 width=1 by lsx_lref_skip/
-  #Hli #Hi elim (drop_O1_lt (Ⓕ) … Hi) -Hi
-  #I #K #V #HLK lapply (csx_inv_lref_bind … HLK … H) -H
-  /4 width=6 by lsx_lref_be, fqup_lref/
-*)
 | #a #I #V #T #HG #HL #HT #H destruct
   elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by lfsx_bind_void/
 | #I #V #T #HG #HL #HT #H destruct
-- 
2.39.2