- some renaming according to the written version of basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
index 1f1ebc834316952f6c2de1dad1e31a14b0b080eb..d84202bbc7a60815b7533b9a6b27c6b1f7507992 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpxs.ma
@@ -12,43 +12,51 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/lpxs_lleq.ma".
 include "basic_2/computation/lpxs_lpxs.ma".
-include "basic_2/computation/lsx.ma".
+include "basic_2/computation/lsx_alt.ma".
 
 (* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
 
 (* Advanced properties ******************************************************)
 
-lemma lsx_lleq_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
-                      ∀L2. L1 ⋕[T, 0] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
-#h #g #T #G #L1 #H @(lsx_ind … H) -L1
-#L1 #_ #IHL1 #L2 #HL12 @lsx_intro
-#K2 #HLK2 #HnLK2 elim (lleq_lpxs_trans … HL12 … HLK2) -HLK2
-/5 width=4 by lleq_canc_sn, lleq_trans/
+fact lsx_bind_lpxs_aux: ∀h,g,a,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
+                        ∀Y,T. G ⊢ ⬊*[h, g, T, ⫯l] Y →
+                        ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
+                        G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L2.
+#h #g #a #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
+#L1 #HL1 #IHL1 #Y #T #H @(lsx_ind_alt … H) -Y
+#Y #HY #IHY #L2 #H #HL12 destruct @lsx_intro_alt
+#L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
+#HL10 #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ]
+[ #HnV elim (lleq_dec V L1 L2 l)
+  [ #HV @(IHL1 … L0) /3 width=5 by lsx_lpxs_trans, lpxs_pair, lleq_canc_sn/ (**) (* full auto too slow *)
+  | -HnV -HL10 /4 width=5 by lsx_lpxs_trans, lpxs_pair/
+  ]
+| /3 width=4 by lpxs_pair/
+]
 qed-.
 
-lemma lsx_lpxs_trans: ∀h,g,T,G,L1. G ⊢ ⋕⬊*[h, g, T] L1 →
-                      ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⋕⬊*[h, g, T] L2.
-#h #g #T #G #L1 #H @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (lleq_dec T L1 L2 0) /3 width=4 by lsx_lleq_trans/
-qed-.
+lemma lsx_bind: ∀h,g,a,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
+                ∀T. G ⊢ ⬊*[h, g, T, ⫯l] L.ⓑ{I}V →
+                G ⊢ ⬊*[h, g, ⓑ{a,I}V.T, l] L.
+/2 width=3 by lsx_bind_lpxs_aux/ qed.
 
-lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V. G ⊢ ⋕⬊*[h, g, V] L1 →
-                     â\88\80L2,T. G â\8a¢ â\8b\95â¬\8a*[h, g, T] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
-                     G â\8a¢ â\8b\95â¬\8a*[h, g, â\93\95{I}T.V] L2.
-#h #g #I #G #L1 #V #H @(lsx_ind … H) -L1
-#L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind … H) -L2
-#L2 #HL2 #IHL2 #HL12 @lsx_intro
+lemma lsx_flat_lpxs: ∀h,g,I,G,L1,V,l. G ⊢ ⬊*[h, g, V, l] L1 →
+                     â\88\80L2,T. G â\8a¢ â¬\8a*[h, g, T, l] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
+                     G â\8a¢ â¬\8a*[h, g, â\93\95{I}V.T, l] L2.
+#h #g #I #G #L1 #V #l #H @(lsx_ind_alt … H) -L1
+#L1 #HL1 #IHL1 #L2 #T #H @(lsx_ind_alt … H) -L2
+#L2 #HL2 #IHL2 #HL12 @lsx_intro_alt
 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
-#HL10 #H elim (nlleq_inv_flat … H) -H [ -HL2 -IHL1 | -HL1 -IHL2 ]
-[ /3 width=1 by/
-| #HnV elim (lleq_dec V L1 L2 0)
+#HL10 #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
+[ #HnV elim (lleq_dec V L1 L2 l)
   [ #HV @(IHL1 … L0) /3 width=3 by lsx_lpxs_trans, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
   | -HnV -HL10 /3 width=4 by lsx_lpxs_trans/
+  ]
+| /3 width=1 by/
 ]
 qed-.
 
-lemma lsx_flat: ∀h,g,I,G,L,V. G ⊢ ⋕⬊*[h, g, V] L →
-                â\88\80T. G â\8a¢ â\8b\95â¬\8a*[h, g, T] L â\86\92 G â\8a¢ â\8b\95â¬\8a*[h, g, â\93\95{I}T.V] L.
+lemma lsx_flat: ∀h,g,I,G,L,V,l. G ⊢ ⬊*[h, g, V, l] L →
+                â\88\80T. G â\8a¢ â¬\8a*[h, g, T, l] L â\86\92 G â\8a¢ â¬\8a*[h, g, â\93\95{I}V.T, l] L.
 /2 width=3 by lsx_flat_lpxs/ qed.