some corrections ...

[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..883e32d0bcb80b0c81b1682f5b93e5b5973d50ea 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_csx.ma
@@ -14,20 +14,83 @@
 
 include "basic_2/computation/lpxs_lleq.ma".
 include "basic_2/computation/csx_alt.ma".
-include "basic_2/computation/lsx.ma".
+include "basic_2/computation/lsx_lpxs.ma".
 
 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
 
-(* Main properties **********************************************************)
+(* Advanced forward lemmas **************************************************)
+
+include "basic_2/computation/cpxs_lleq.ma".
+
+(*
+lemma lsx_cpxs_conf: ∀h,g,G,L1,T1,T2. G ⊢ ⋕⬊*[h, g, T1] L1 →
+                     ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2 →
+                     G ⊢ ⋕⬊*[h, g, T2] L2.
+#h #g #G #L1 #T1 #T2 #H @(lsx_ind … H) -L1
+#L1 #HL1 #IHL1 #L2 #HL12 #HT12 @lsx_intro
+#L3 #HL23 #HnL23 elim (lleq_dec T2 L1 L2 0) [| -HnL23 ]
+[ #HT2 @(IHL1 L3) /2 width=3 by lpxs_trans/
+
+ @(lsx_lpxs_trans … HL23) 
+| #HnT2 @(lsx_lpxs_trans … HL23) @(IHL1 … L2) //
+  #HT1 @HnT2 @(lleq_cpxs_conf_dx … HT12) //
+]
+*)
+
+lemma lsx_fwd_bind_dx_lpxs: ∀h,g,a,I,G,L1,V1. ⦃G, L1⦄ ⊢ ⬊*[h, g] V1 →
+                            ∀L2,T. G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V1.T] L2 → 
+                            ∀V2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L2⦄ ⊢ V1 ➡*[h, g] V2 →
+                            G ⊢ ⋕⬊*[h, g, T] L2.ⓑ{I}V2.
+#h #g #a #I #G #L1 #V1 #H @(csx_ind_alt … H) -V1
+#V1 #_ #IHV1 #L2 #T #H @(lsx_ind … H) -L2
+#L2 #HL2 #IHL2 #V2 #HL12 #HV12 @lsx_intro
+#Y #H #HnT elim (lpxs_inv_pair1 … H) -H
+#L3 #V3 #HL23 #HV23 #H destruct
+lapply (lpxs_trans … HL12 … HL23) #HL13
+elim (eq_term_dec V2 V3)
+[ (* -HV13 -HL2 -IHV1 -HL12 *) #H destruct
+  @IHL2 -IHL2 // -HL23 -HL13 /3 width=2 by lleq_fwd_bind_O/
+| -IHL2 -HnT #HnV23 elim (eq_term_dec V1 V2)
+  [ #H -HV12 destruct
+  (*  @(lsx_lpxs_trans … (L2.ⓑ{I}V2)) /2 width=1 by lpxs_pair/ *)
+    @(IHV1 … HnV23) -IHV1 -HnV23 /2 width=3 by lpxs_cpxs_trans/ -HL12 -HL13
+  @(lsx_lpxs_trans … HL23)
 
-axiom csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → G ⊢ ⋕⬊*[h, g, T] L.
 
-axiom lsx_inv_csx: ∀h,g,G,L,T. G ⊢ ⋕⬊*[h, g, T] L → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+lemma lsx_fwd_bind_dx_lpxs: ∀h,g,a,I,G,L1,V. ⦃G, L1⦄ ⊢ ⬊*[h, g] V →
+                            ∀L2,T. G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
+                            G ⊢ ⋕⬊*[h, g, T] L2.ⓑ{I}V.
+#h #g #a #I #G #L1 #V #H @(csx_ind_alt … H) -V
+#V1 #_ #IHV1 #L2 #T #H @(lsx_ind … H) -L2
+#L2 #HL2 #IHL2 #HL12 @lsx_intro
+#Y #H #HnT elim (lpxs_inv_pair1 … H) -H
+#L3 #V3 #HL23 #HV13 #H destruct
+lapply (lpxs_trans … HL12 … HL23) #HL13
+elim (eq_term_dec V1 V3)
+[ -HV13 -HL2 -IHV1 -HL12 #H destruct
+  @IHL2 -IHL2 // -HL23 -HL13 /3 width=2 by lleq_fwd_bind_O/
+| -IHL2 -HnT #HnV13
+  @(IHV1 … HnV13) -IHV1 -HnV13 /2 width=3 by lpxs_cpxs_trans/ -HL12 -HL13
+  @(lsx_lpxs_trans … HL23)
 
+
+(* Advanced inversion lemmas ************************************************)
+
+
+
+(* Main properties **********************************************************)
+
+axiom csx_lsx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → G ⊢ ⋕⬊*[h, g, T] L.
 (*
-#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  
+#h #g #G #L #T @(fqup_wf_ind_eq … G L T) -G -L -T
+#G1 #L1 #T1 #IH #G2 #L2 * *
+[ #k #HG #HL #HT destruct //
+| #i #HG #HL #HT destruct
+  #H
+| #p #HG #HL #HT destruct //
+| #a #I #V2 #T2 #HG #HL #HT #H destruct
+  elim (csx_fwd_bind … H) -H
+  #HV2 #HT2
+| #I #V2 #T2 #HG #HL #HT #H destruct
+  elim (csx_fwd_flat … H) -H /3 width=1 by lsx_flat/
 *)