X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flsx_csx.ma;h=67f754b7bb918c0bfcf7a71ef34a25072f1cc49d;hb=fb5c93c9812ea39fb78f1470da2095c80822e158;hp=61dca7f92bca95facaf4073c462ed0e41ed0e75b;hpb=f7994db705d6c1200cc3e9f1827b7d9f6d0ad001;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
index 61dca7f92..67f754b7b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
@@ -13,48 +13,47 @@
 (**************************************************************************)
 
 include "basic_2/computation/csx_lpxs.ma".
-include "basic_2/computation/lcosx_cpxs.ma".
+include "basic_2/computation/lcosx_cpx.ma".
 
 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
 
 (* Advanced properties ******************************************************)
 
-lemma lsx_lref_be_lpxs: ∀h,g,I,G,K1,V,i,d. d ≤ yinj i → ⦃G, K1⦄ ⊢ ⬊*[h, g] V →
-                        ∀K2. G ⊢ ⋕⬊*[h, g, V, 0] K2 → ⦃G, K1⦄ ⊢ ➡*[h, g] K2 →
-                        ∀L2. ⇩[i] L2 ≡ K2.ⓑ{I}V → G ⊢ ⋕⬊*[h, g, #i, d] L2.
-#h #g #I #G #K1 #V #i #d #Hdi #H @(csx_ind_alt … H) -V
+lemma lsx_lref_be_lpxs: ∀h,g,I,G,K1,V,i,l. l ≤ yinj i → ⦃G, K1⦄ ⊢ ⬊*[h, g] V →
+                        ∀K2. G ⊢ ⬊*[h, g, V, 0] K2 → ⦃G, K1⦄ ⊢ ➡*[h, g] K2 →
+                        ∀L2. ⬇[i] L2 ≡ K2.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, l] L2.
+#h #g #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 (lpxs_ldrop_conf … HLK0 … HL02) -HL02
-#Y #H #HLK2 elim (lpxs_inv_pair1 … H) -H
+#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
-lapply (lpxs_trans … HK10 … HK02) #HK12
-elim (eq_term_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 -HK10 | -IHK0 -HnL02 -HLK0 ]
-[ /4 width=8 by lleq_lref/
-| @(IHV0 … HnV02 … HK12 … HLK2) -IHV0 -HnV02 -HK12 -HLK2
-  /3 width=4 by lsx_cpxs_trans_O, lsx_lpxs_trans, lpxs_cpxs_trans/ (**) (* full auto too slow *)
+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 *)
 ]
 qed.
 
-lemma lsx_lref_be: ∀h,g,I,G,K,V,i,d. d ≤ yinj i → ⦃G, K⦄ ⊢ ⬊*[h, g] V →
-                   G ⊢ ⋕⬊*[h, g, V, 0] K →
-                   ∀L. ⇩[i] L ≡ K.ⓑ{I}V → G ⊢ ⋕⬊*[h, g, #i, d] L.
+lemma lsx_lref_be: ∀h,g,I,G,K,V,i,l. l ≤ yinj i → ⦃G, K⦄ ⊢ ⬊*[h, g] V →
+                   G ⊢ ⬊*[h, g, V, 0] K →
+                   ∀L. ⬇[i] L ≡ K.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, l] L.
 /2 width=8 by lsx_lref_be_lpxs/ qed.
 
 (* Main properties **********************************************************)
 
-theorem csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀d. G ⊢ ⋕⬊*[h, g, T, d] L.
+theorem csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀l. G ⊢ ⬊*[h, g, T, l] L.
 #h #g #G #L #T @(fqup_wf_ind_eq … G L T) -G -L -T
 #Z #Y #X #IH #G #L * * //
-[ #i #HG #HL #HT #H #d destruct
+[ #i #HG #HL #HT #H #l destruct
   elim (lt_or_ge i (|L|)) /2 width=1 by lsx_lref_free/
-  elim (ylt_split i d) /2 width=1 by lsx_lref_skip/
-  #Hdi #Hi elim (ldrop_O1_lt … Hi) -Hi
+  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 #d destruct
+| #a #I #V #T #HG #HL #HT #H #l destruct
   elim (csx_fwd_bind … H) -H /3 width=1 by lsx_bind/
-| #I #V #T #HG #HL #HT #H #d destruct
+| #I #V #T #HG #HL #HT #H #l destruct
   elim (csx_fwd_flat … H) -H /3 width=1 by lsx_flat/
 ]
 qed.