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 ff005164fb89a0650b3aa1a9d3df536e3e65a5a5..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
@@ -12,53 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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_lfpxs.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 ****)
-(*
+
 (* 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.
-#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
-#L2 #HL02 #HnL02 elim (lpx_drop_conf … HLK0 … HL02) -HL02
-#Y #H #HLK2 elim (lpx_inv_pair1 … H) -H
-#K2 #V2 #HK02 #HV02 #H destruct
-elim (eq_term_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnL02 -HLK0 ]
-[ /4 width=8 by lpxs_strap1, lleq_lref/
-| @(IHV0 … HnV02 … HLK2) -IHV0 -HnV02 -HLK2
-  /3 width=4 by lsx_cpx_trans_O, lsx_lpx_trans, lpxs_cpx_trans, lpxs_strap1/ (**) (* full auto too slow *)
+(* Basic_2A1: uses: lsx_lref_be_lpxs *)
+lemma lfsx_pair_lpxs: ∀h,o,G,K1,V. ⦃G, K1⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ →
+                      ∀K2. G ⊢ ⬈*[h, o, V] 𝐒⦃K2⦄ → ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
+                      ∀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_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_step_dx, lfdeq_pair/
+| @(IHV0 … HnV02) -IHV0 -HnV02
+  [ /2 width=3 by lpxs_cpx_trans/
+  | /3 width=3 by lfsx_lpx_trans, lfsx_cpx_trans/
+  | /2 width=3 by lpxs_step_dx/
+  ]
+]
+qed.
+
+(* Basic_2A1: uses: lsx_lref_be *)
+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.
 
-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.
-*)
 (* 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 [ |*: * ]
-  [ #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_drops, 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
+| #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/