notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsx_csx.ma

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 48786e5e2cc48ec96ff4e53a292310b86fabcf3b..a4937895565993723302de6d6ffb95328d416e76 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
@@ -12,22 +12,48 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/lpxs_lleq.ma".
-include "basic_2/computation/csx_alt.ma".
-include "basic_2/computation/lsx.ma".
+include "basic_2/computation/csx_lpxs.ma".
+include "basic_2/computation/lcosx_cpx.ma".
 
 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
 
-(* Main properties **********************************************************)
+(* 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
+#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 *)
+]
+qed.
 
-axiom csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → G ⊢ ⋕⬊*[h, g, T] L.
+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.
+/2 width=8 by lsx_lref_be_lpxs/ qed.
 
-axiom lsx_inv_csx: ∀h,g,G,L,T. G ⊢ ⋕⬊*[h, g, T] L → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+(* Main properties **********************************************************)
 
-(*
-#h #g #G #L1 #T1 #H @(csx_ind_alt … H) -T1
-#T1 #_ #IHT1 @lsx_intro
-#L2 #HL12 #HnT1 elim (lpxs_inv_cpxs_nlleq … HL12 HnT1) -HL12 -HnT1
-#T2 #H1T12 #HnT12 #H2T12 lapply (IHT1 … H1T12 HnT12) -IHT1 -H1T12 -HnT12
-#HT2  
-*)
+theorem csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀d. G ⊢ ⬊*[h, g, T, d] 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
+  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 (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
+  elim (csx_fwd_bind … H) -H /3 width=1 by lsx_bind/
+| #I #V #T #HG #HL #HT #H #d destruct
+  elim (csx_fwd_flat … H) -H /3 width=1 by lsx_flat/
+]
+qed.