second recursive part of preservation finally proved!

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 7f325d41a40395a48c39d8a8ffc0d73b03256d29..1d5f93c49dc5c227129c1dee242c7523eaddca8e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/ssta_ssta.ma".
+include "basic_2/unwind/sstas_sstas.ma".
 include "basic_2/computation/ygt.ma".
 include "basic_2/equivalence/cpcs_ltpr.ma".
 include "basic_2/dynamic/snv_ltpss_dx.ma".
@@ -140,13 +140,16 @@ lapply (ltpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
 lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
 elim (cpcs_inv_cprs … H) -H /3 width=3/
 qed-.
-(*
-fact sstas_dxprs_aux: ∀h,g,L0,T0.
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
-                      ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊩ T1 :[g] →
-                      ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → ∀T2. ⦃h, L1⦄ ⊢ T1 •*➡*[g] T2 →
-                      ∃∃U2. ⦃h, L1⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ⬌* U2.
-#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #HTU1 #T2 * #T #HT1T #HTT2
-*)
+
+fact ssta_dxprs_aux: ∀h,g,L0,T0.
+                     (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
+                     (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
+                     ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊩ T1 :[g] →
+                     ∀l,U1. ⦃h, L1⦄ ⊢ T1 •[g, l+1] U1 → ∀T2. ⦃h, L1⦄ ⊢ T1 •*➡*[g] T2 →
+                     ∃∃U,U2. ⦃h, L1⦄ ⊢ U1 •*[g] U & ⦃h, L1⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U ⬌* U2.
+#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #l #U1 #HTU1 #T2 * #T #HT1T #HTT2
+elim (sstas_strip … HT1T … HTU1) #HU1T destruct [ -HT1T | -L0 -T0 -T1 ]
+[ elim (ssta_ltpr_cprs_aux … IH2 IH1 … HTU1 L1 … HTT2) // -L0 -T0 -T /3 width=5/
+| @(ex3_2_intro …T2 HU1T) // /2 width=1/
+]
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma
index 2bee82488cfca6e682f7f849d4d5f104b375183d..f32e1ba015eba4646014b948a8751fecdff80769 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma
@@ -18,21 +18,36 @@ include "basic_2/dynamic/snv_cpcs.ma".
 
 (* Properties on stratified static type assignment for terms ****************)
 
-fact snv_ssta_aux: ∀h,g,L,T. (
-                      ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
-                      ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
-                      ♯{L0, T0} < ♯{L, T} → ⦃h, L0⦄ ⊩ U0 :[g]
-                   ) →
-                   ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
-                   ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
-                   L0 = L → T0 = T → ⦃h, L0⦄ ⊩ U0 :[g].
-#h #g #L #T #IH1 #L0 #T0 * -L0 -T0
-[
-|
-|
-| #a #L0 #V #W #W0 #T0 #V0 #l0 #HV #HT0 #HVW #HW0 #HTV0 #X #l #H #H1 #H2 destruct
-  elim (ssta_inv_appl1 … H) -H #U0 #HTU0 #H destruct
-  lapply (IH1 … HT0 … HTU0 ?) // #HU0
-  @(snv_appl … HV HU0 HVW HW0) -HV -HU0 -HVW -HW0
-| #L0 #W #T0 #W0 #l0 #_ #HT0 #_ #_ #U0 #l #H #H1 #H2 destruct -W0
-  lapply (ssta_inv_cast1 … H) -H /2 width=5/
+fact snv_ssta_aux: ∀h,g,L0,T0.
+                   (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
+                   (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
+                   (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
+                   ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_ssta h g L1 T1.
+#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 * * [||||*]
+[ #k #HL0 #HT0 #_ #X #l #H2 destruct -IH3 -IH2 -IH1
+  elim (ssta_inv_sort1 … H2) -H2 #_ #H destruct //
+| #i #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2
+  elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1
+  elim (ssta_inv_lref1 … H2) -H2 * #K0 #V0 #W1 [| #l ] #H #HVW1 #HX [| #_ ]
+  lapply (ldrop_mono … H … HLK1) -H #H destruct
+  lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) #H
+  lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 /4 width=7/
+| #p #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2 -IH1
+  elim (snv_inv_gref … H1)
+| #a #I #V1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2
+  elim (snv_inv_bind … H1) -H1 #HV1 #HT1
+  elim (ssta_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct /4 width=5/
+| #V1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct
+  elim (snv_inv_appl … H1) -H1 #a #W1 #W0 #T0 #l0 #HV1 #HT1 #HVW1 #HW10 #HT10
+  elim (ssta_inv_appl1 … H2) -H2 #U1 #HTU1 #H destruct
+  lapply (IH1 … HT1 … HTU1) -IH1 /2 width=1/ #HU1
+  elim (ssta_dxprs_aux … IH3 IH2 … HTU1 … HT10) -IH3 -IH2 // /2 width=2/ -T1 #U #X #HU1U #H #HU0
+  elim (sstas_inv_bind1 … H) -H #U0 #HTU0 #H destruct
+  elim (cpcs_inv_abst2 … HU0) -HU0 #W2 #U2 #HU2 #HU02
+  elim (cprs_inv_abst … HU02 Abst W0) -HU02 #HW02 #_
+  lapply (cprs_trans … HW10 … HW02) -W0 /3 width=10 by snv_appl, ex2_intro/ (**) (* auto is too slow without trace *)
+| #W1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2
+  elim (snv_inv_cast … H1) -H1 #U1 #l0 #HW1 #HT1 #HTU1 #HUW1 
+  lapply (ssta_inv_cast1 … H2) -H2 /3 width=5/
+]
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
index f11a078bfb07f912b4bb32608da9fa6fb480c9ea..84b9412327283d0a750d687703c45061375645f3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
@@ -30,7 +30,7 @@ qed-.
 
 lemma sstas_strip: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
                    ∀U2,l. ⦃h, L⦄ ⊢ T •[g, l] U2 →
-                   ⦃h, L⦄ ⊢ U1 •[g, l] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
+                   T = U1 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
 #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
 #T #U #l0 #HTU #HU1 #_ #U2 #l #H2
 elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
@@ -47,5 +47,8 @@ theorem sstas_conf: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
                    ⦃h, L⦄ ⊢ U1 •*[g] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
 #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
 #T #U #l #HTU #HU1 #IHU1 #U2 #H2
-elim (sstas_strip … H2 … HTU) -T /2 width=1/ -IHU1 /3 width=4/
+elim (sstas_strip … H2 … HTU) #H destruct
+[ -H2 -IHU1 /3 width=4/
+| -T /2 width=1/
+]
 qed-.