From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 10 Jun 2014 18:53:36 +0000 (+0000)
Subject: preservation of stratified vaildity through ordinary reduction and static typing
X-Git-Tag: make_still_working~904
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=4720368dcf18593959c6d21484f62fb5b61f3d26;p=helm.git

preservation of stratified vaildity through ordinary reduction and static typing
---

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
index 56ed1c2c5..e73f809fc 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
@@ -83,7 +83,7 @@ fact ssta_cpr_lpr_aux: ∀h,g,G0,L0,T0.
                        ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
                        ∃∃U2. ⦃G, L2⦄ ⊢ T2 •[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
 #h #g #G0 #L0 #T0 #IH #G #L1 #T1 #H01 #HT1 #l #Hl #U1 #HTU1 #T2 #HT12 #L2 #HL12
-elim (IH … H01 … 1 … Hl U1 … HT12 … HL12)
+elim (IH … H01 … 1 … Hl U1 … HT12 … HL12) -H01 -Hl -HT12 -HL12
 /3 width=3 by lsstas_inv_SO, ssta_lsstas, ex2_intro/
 qed-.
 
@@ -104,7 +104,7 @@ elim (IH1 … Hl21 … HTU … HTT2 … HL12) -IH1 -HTU -HTT2
 [2: /3 width=12 by da_cprs_lpr_aux/
 |3: /3 width=10 by snv_cprs_lpr_aux/
 |4: /3 width=5 by fpbg_fpbs_trans, cprs_fpbs/
-] -G0 -L0 -T0 -T1 -T -l1 #U2 #HTU2 #HU2
+] -G0 -L0 -T0 -T1 -T -l1
 /4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/
 qed-.
 
@@ -144,13 +144,12 @@ fact lsstas_cpds_aux: ∀h,g,G0,L0,T0.
 lapply (da_mono … H … Hl1) -H #H destruct
 lapply (lsstas_da_conf … HTU1 … Hl1) #Hl12
 elim (le_or_ge l2 l) #Hl2
-[ lapply (lsstas_conf_le … HTU1 … HT1T) -HT1T // #HU1T
+[ lapply (lsstas_conf_le … HTU1 … HT1T) -HT1T
   /5 width=11 by cpds_cpes_dx, monotonic_le_minus_l, ex3_2_intro, ex4_3_intro/
 | lapply (lsstas_da_conf … HT1T … Hl1) #Hl1l
   lapply (lsstas_conf_le … HT1T … HTU1) -HTU1 // #HTU1
-  elim (lsstas_cprs_lpr_aux … IH3 IH2 IH1 … Hl1l … HTU1 … HTT2 L)
-  /3 width=8 by fpbg_fpbs_trans, lsstas_fpbs, monotonic_le_minus_l/ -T #U2 #HTU2 #HU12
-  /3 width=5 by cpcs_cpes, ex3_2_intro/
+  elim (lsstas_cprs_lpr_aux … IH3 IH2 IH1 … Hl1l … HTU1 … HTT2 L) -IH3 -IH2 -IH1 -Hl1l -HTU1 -HTT2
+  /3 width=8 by cpcs_cpes, fpbg_fpbs_trans, lsstas_fpbs, monotonic_le_minus_l, ex3_2_intro/
 ]
 qed-.
 
@@ -163,7 +162,7 @@ fact cpds_cpr_lpr_aux: ∀h,g,G0,L0,T0.
                        ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2.
 #h #g #G0 #L0 #T0 #IH2 #IH1 #G #L1 #T1 #H01 #HT1 #U1 * #W1 #l1 #l2 #Hl21 #Hl1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12
 elim (IH1 … H01 … HTW1 … HT12 … HL12) -IH1 // #W2 #HTW2 #HW12
-lapply (IH2 … H01 … Hl1 … HT12 … HL12) -L0 -T0 // -T1 #Hl1
+lapply (IH2 … H01 … Hl1 … HT12 … HL12) -L0 -T0 // -T1
 lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
 lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
 elim (cpcs_inv_cprs … H) -H /3 width=7 by ex4_3_intro, ex2_intro/
diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma
new file mode 100644
index 000000000..57d18eef2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma
@@ -0,0 +1,146 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/computation/fsb_aaa.ma".
+include "basic_2/dynamic/snv_da_lpr.ma".
+include "basic_2/dynamic/snv_lsstas.ma".
+include "basic_2/dynamic/snv_lsstas_lpr.ma".
+include "basic_2/dynamic/snv_lpr.ma".
+
+(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
+
+(* Main preservation properties *********************************************)
+
+lemma snv_preserve: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
+                    ∧∧ IH_da_cpr_lpr h g G L T
+                     & IH_snv_cpr_lpr h g G L T
+                     & IH_snv_lsstas h g G L T
+                     & IH_lsstas_cpr_lpr h g G L T.
+#h #g #G #L #T #HT elim (snv_fwd_aaa … HT) -HT
+#A #HT @(aaa_ind_fpbg h g … HT) -G -L -T -A
+#G #L #T #A #_ #IH -A @and4_intro
+[ letin aux ≝ da_cpr_lpr_aux | letin aux ≝ snv_cpr_lpr_aux
+| letin aux ≝ snv_lsstas_aux | letin aux ≝ lsstas_cpr_lpr_aux
+]
+@(aux … G L T) // #G0 #L0 #T0 #H elim (IH … H) -IH -H //
+qed-.
+
+theorem da_cpr_lpr: ∀h,g,G,L,T. IH_da_cpr_lpr h g G L T.
+#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
+qed-.
+
+theorem snv_cpr_lpr: ∀h,g,G,L,T. IH_snv_cpr_lpr h g G L T.
+#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
+qed-.
+
+theorem snv_lsstas: ∀h,g,G,L,T. IH_snv_lsstas h g G L T.
+#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/
+qed-.
+
+theorem lsstas_cpr_lpr: ∀h,g,G,L,T. IH_lsstas_cpr_lpr h g G L T.
+#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/
+qed-.
+
+(* Advanced preservation properties *****************************************)
+
+lemma snv_cprs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, g].
+#h #g #G #L1 #T1 #HT1 #T2 #H
+@(cprs_ind … H) -T2 /3 width=5 by snv_cpr_lpr/
+qed-.
+
+lemma da_cprs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                   ∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l →
+                   ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, g] l.
+#h #g #G #L1 #T1 #HT1 #l #Hl #T2 #H
+@(cprs_ind … H) -T2 /3 width=6 by snv_cprs_lpr, da_cpr_lpr/
+qed-.
+
+lemma da_cpcs: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
+               ∀T2. ⦃G, L⦄ ⊢ T2 ¡[h, g] →
+               ∀l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ∀l2. ⦃G, L⦄ ⊢ T2 ▪[h, g] l2 →
+               ⦃G, L⦄ ⊢ T1 ⬌* T2 → l1 = l2.
+#h #g #G #L #T1 #HT1 #T2 #HT2 #l1 #Hl1 #l2 #Hl2 #H
+elim (cpcs_inv_cprs … H) -H /3 width=12 by da_cprs_lpr, da_mono/
+qed-.
+
+lemma ssta_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                    ∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l+1 →
+                    ∀U1. ⦃G, L1⦄ ⊢ T1 •[h, g] U1 →
+                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                    ∃∃U2. ⦃G, L2⦄ ⊢ T2 •[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #g #G #L1 #T1 #HT1 #l #Hl #U1 #HTU1 #T2 #HT12 #L2 #HL12
+elim (lsstas_cpr_lpr  … 1 … Hl U1 … HT12 … HL12) -Hl -HT12 -HL12
+/3 width=3 by lsstas_inv_SO, ssta_lsstas, ex2_intro/
+qed-.
+
+lemma lsstas_cprs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                       ∀l1,l2. l2 ≤ l1 → ⦃G, L1⦄ ⊢ T1 ▪[h, g] l1 →
+                       ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, g, l2] U1 →
+                       ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                       ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, g, l2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #g #G #L1 #T1 #HT1 #l1 #l2 #Hl21 #Hl1 #U1 #HTU1 #T2 #H
+@(cprs_ind … H) -T2 [ /2 width=9 by lsstas_cpr_lpr/ ]
+#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12
+elim (IHT1 L1) // -IHT1 #U #HTU #HU1
+elim (lsstas_cpr_lpr … Hl21 … HTU … HTT2 … HL12) -HTU -HTT2
+[2,3: /2 width=6 by snv_cprs_lpr, da_cprs_lpr/ ] -T1 -T -l1
+/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/
+qed-.
+
+lemma lsstas_cpcs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                       ∀l,l1. l ≤ l1 → ⦃G, L1⦄ ⊢ T1 ▪[h, g] l1 → ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, g, l] U1 →
+                       ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, g] →
+                       ∀l2. l ≤ l2 → ⦃G, L1⦄ ⊢ T2 ▪[h, g] l2 → ∀U2. ⦃G, L1⦄ ⊢ T2 •*[h, g, l] U2 →
+                       ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #g #G #L1 #T1 #HT1 #l #l1 #Hl1 #HTl1 #U1 #HTU1 #T2 #HT2 #l2 #Hl2 #HTl2 #U2 #HTU2 #H #L2 #HL12
+elim (cpcs_inv_cprs … H) -H #T #H1 #H2
+elim (lsstas_cprs_lpr … HT1 … Hl1 HTl1 … HTU1 … H1 … HL12) -T1 #W1 #H1 #HUW1
+elim (lsstas_cprs_lpr … HT2 … Hl2 HTl2 … HTU2 … H2 … HL12) -T2 #W2 #H2 #HUW2
+lapply (lsstas_mono … H1 … H2) -h -T -l #H destruct /2 width=3 by cpcs_canc_dx/
+qed-.
+
+lemma snv_ssta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
+                ∀l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 →
+                ∀U. ⦃G, L⦄ ⊢ T •[h, g] U → ⦃G, L⦄ ⊢ U ¡[h, g].
+/3 width=7 by lsstas_inv_SO, ssta_lsstas, snv_lsstas/ qed-.
+
+lemma lsstas_cpds: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
+                   ∀l1,l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
+                   ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] U1 → ∀T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 →
+                   ∃∃U2,l. l ≤ l2 & ⦃G, L⦄ ⊢ T2 •*[h, g, l] U2 & ⦃G, L⦄ ⊢ U1 •*⬌*[h, g] U2.
+#h #g #G #L #T1 #HT1 #l1 #l2 #Hl21 #Hl1 #U1 #HTU1 #T2 * #T #l0 #l #Hl0 #H #HT1T #HTT2
+lapply (da_mono … H … Hl1) -H #H destruct
+lapply (lsstas_da_conf … HTU1 … Hl1) #Hl12
+elim (le_or_ge l2 l) #Hl2
+[ lapply (lsstas_conf_le … HTU1 … HT1T) -HT1T //
+  /5 width=11 by cpds_cpes_dx, monotonic_le_minus_l, ex3_2_intro, ex4_3_intro/
+| lapply (lsstas_da_conf … HT1T … Hl1) #Hl1l
+  lapply (lsstas_conf_le … HT1T … HTU1) -HTU1 // #HTU1
+  elim (lsstas_cprs_lpr … Hl1l … HTU1 … HTT2 L) -Hl1l -HTU1 -HTT2
+  /3 width=7 by snv_lsstas, cpcs_cpes, monotonic_le_minus_l, ex3_2_intro/
+]
+qed-.
+
+lemma cpds_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                    ∀U1. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] U1 →
+                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                    ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2.
+#h #g #G #L1 #T1 #HT1 #U1 * #W1 #l1 #l2 #Hl21 #Hl1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12
+elim (lsstas_cpr_lpr … HTW1 … HT12 … HL12) // #W2 #HTW2 #HW12
+lapply (da_cpr_lpr … Hl1 … HT12 … HL12) // -T1
+lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
+lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
+elim (cpcs_inv_cprs … H) -H /3 width=7 by ex4_3_intro, ex2_intro/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
index 5f82638e0..ef23ce149 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
@@ -27,6 +27,7 @@ lapply (ldrop_fwd_length_lt2 … HLK1) -K1
 /5 width=3 by ylt_yle_trans, ylt_inj, or3_intro0, and3_intro/
 qed.
 
+(* Note: lemma 1400 concludes the "big tree" theorem *)
 lemma llor_total: ∀L1,L2,T,d. |L1| = |L2| → ∃L. L1 ⩖[T, d] L2 ≡ L.
 #L1 @(lenv_ind_alt … L1) -L1
 [ #L2 #T #d #H >(length_inv_zero_sn … H) -L2 /2 width=2 by ex_intro/
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 0abb6cb23..db46ed578 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -44,7 +44,7 @@ table {
           }
         ]
         [ { "stratified native validity" * } {
-             [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_da_lpr" + "snv_aaa" + "snv_lsstas" + "snv_lsstas_lpr" + "snv_lpr" + "snv_cpcs" * ]
+             [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_da_lpr" + "snv_aaa" + "snv_lsstas" + "snv_lsstas_lpr" + "snv_lpr" + "snv_cpcs" + "snv_preserve" * ]
           }
         ]
      }