long awaited update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfsx_csx.ma

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 eb44187778f57086c17b996017d9831bce0c42a7..5310d8ab791aac77a0b133907090ed8a605fee55 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_csx.ma
@@ -11,17 +11,15 @@
 (*        v         GNU General Public License Version 2                  *)
 (*                                                                        *)
 (**************************************************************************)
-(*
+
+include "basic_2/rt_computation/lpxs_lpx.ma".
+include "basic_2/rt_computation/lpxs_cpxs.ma".
 include "basic_2/rt_computation/csx_cpxs.ma".
 include "basic_2/rt_computation/csx_lsubr.ma".
-include "basic_2/rt_computation/lfsx_lpxs.ma".
-*)
+include "basic_2/rt_computation/lfsx_lpx.ma".
 include "basic_2/rt_computation/lsubsx_lfsx.ma".
 
 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
-(*
-axiom lpxs_trans: ∀h,G. Transitive … (lpxs h G).
-*)
 
 (* Advanced properties ******************************************************)
 
@@ -31,46 +29,43 @@ lemma lfsx_pair_lpxs: ∀h,o,G,K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
                       ∀I. G ⊢ ⬈*[h, o, #0] 𝐒⦃K2.ⓑ{I}V⦄.
 #h #o #G #K1 #V #H
 @(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
-@(lfsx_ind_lpxs … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
-@lfsx_intro_lpxs #Y #HY #HnY
-elim (lpxs_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
+@(lfsx_ind_lpx … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
+@lfsx_intro_lpx #Y #HY #HnY
+elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
 elim (tdeq_dec h o V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
-[ /5 width=5 by lfsx_lfdeq_trans, lpxs_trans, lfdeq_pair/
+[ /5 width=5 by lfsx_lfdeq_trans, lpxs_step_dx, lfdeq_pair/
 | @(IHV0 … HnV02) -IHV0 -HnV02
-  [
-  | /3 width=3 by lfsx_lpxs_trans, lfsx_cpxs_trans/
-  | /2 width=3 by lpxs_trans/
+  [ /2 width=3 by lpxs_cpx_trans/
+  | /3 width=3 by lfsx_lpx_trans, lfsx_cpx_trans/
+  | /2 width=3 by lpxs_step_dx/
   ]
-
-(*
- @(lfsx_lpxs_trans … (K0.ⓑ{I}V2))
-  [ @(IHV0 … HnV02 … HK10) -IHV0 -HnV02
-    [
-    | /2 width=3 by lfsx_cpxs_trans/
-    ]
-  | 
-  ]  
-*)
+]
+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/
+lemma lfsx_lref_pair_drops: ∀h,o,G,K,V. ⦃G, K⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄ →
+                            ∀I,i,L. ⬇*[i] L ≡ K.ⓑ{I}V → G ⊢ ⬈*[h, o, #i] 𝐒⦃L⦄.
+#h #o #G #K #V #HV #HK #I #i elim i -i
+[ #L #H >(drops_fwd_isid … H) -H /2 width=3 by lfsx_pair_lpxs/
+| #i #IH #L #H
+  elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
+  @(lfsx_lifts … (𝐔❴1❵)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
+]
 qed.
 
 (* Main properties **********************************************************)
 
-theorem csx_lsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
+(* Basic_2A1: uses: csx_lsx *)
+theorem csx_lfsx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
 #h #o #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
 #Z #Y #X #IH #G #L * * //
 [ #i #HG #HL #HT #H destruct
   elim (csx_inv_lref … H) -H [ |*: * ]
   [ /2 width=1 by lfsx_lref_atom/
   | /2 width=3 by lfsx_lref_unit/
-  | /4 width=6 by lfsx_lref_pair, fqup_lref/
+  | /4 width=6 by lfsx_lref_pair_drops, fqup_lref/
   ]
-| #a #I #V #T #HG #HL #HT #H destruct
+| #p #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
   elim (csx_fwd_flat … H) -H /3 width=1 by lfsx_flat/