- lambdadelta: third recursive part of preservation finally proved!

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv_cpcs.ma

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..12c2bf8f5402b87926b7ed84403f4cc005afa116 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
@@ -12,11 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/ssta_ssta.ma".
-include "basic_2/computation/ygt.ma".
+include "basic_2/unwind/sstas_sstas.ma".
 include "basic_2/equivalence/cpcs_ltpr.ma".
 include "basic_2/dynamic/snv_ltpss_dx.ma".
 include "basic_2/dynamic/snv_sstas.ma".
+include "basic_2/dynamic/ygt.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
 
@@ -36,6 +36,12 @@ definition IH_snv_ssta: ∀h:sh. sd h → relation2 lenv term ≝
                         λh,g,L1,T1. ⦃h, L1⦄ ⊩ T1 :[g] →
                         ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] U1 → ⦃h, L1⦄ ⊩ U1 :[g].
 
+(* Properties for the preservation results **********************************)
+
+definition IH_snv_lsubsv: ∀h:sh. sd h → relation2 lenv term ≝
+                          λh,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
+                          ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
+
 fact snv_ltpr_cpr_aux: ∀h,g,L1,T1. IH_snv_ltpr_tpr h g L1 T1 →
                        ⦃h, L1⦄ ⊩ T1 :[g] →
                        ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 → ⦃h, L2⦄ ⊩ T2 :[g].
@@ -140,13 +146,16 @@ 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-.