- lambdadelta: third recursive part of preservation finally proved!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
index 18ca504d493d935a64db5494174964fedb3661f8..1482dd986641ab3c13a9b46e5bcf99b3df41404d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
@@ -12,45 +12,49 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/computation/dxprs_dxprs.ma".
 include "basic_2/dynamic/lsubsv_ldrop.ma".
+include "basic_2/dynamic/lsubsv_dxprs.ma".
 include "basic_2/dynamic/lsubsv_cpcs.ma".
-(*
-include "basic_2/dynamic/lsubsv_ssta.ma".
-*)
+
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
 (* Properties concerning stratified native validity *************************)
-(*
-axiom lsubsv_xprs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
-                         ∀T1,T2. ⦃h, L2⦄ ⊢ T1 •➡*[g] T2 → ⦃h, L1⦄ ⊢ T1 •➡*[g] T2.
 
-/3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
-*)
-lemma lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
-                        ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
-#h #g #L2 #T #H elim H -L2 -T //
-[ #I2 #L2 #K2 #W2 #i #HLK2 #_ #IHW2 #L1 #HL12
-  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
-  elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHW2 ]
-  [ #HK12 #H destruct /3 width=5/
-  | #W1 #V1 #l #HV1 #_ #_ #_ #_ #H #_ destruct /2 width=5/
+fact snv_lsubsv_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. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
+                     ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_lsubsv h g L1 T1.
+#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 * * [||||*] //
+[ #i #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
+  elim (snv_inv_lref … H) -H #I2 #K2 #W2 #HLK2 #HW2
+  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -HL12 #X #H #HLK1
+  lapply (ldrop_pair2_fwd_fw … HLK2 (#i)) -HLK2 #HLK2
+  elim (lsubsv_inv_pair2 … H) -H * #K1
+  [ #HK12 #H destruct /4 width=8 by snv_lref, fw_ygt/ (**) (* auto too slow without trace *)
+  | #W1 #V1 #V2 #l #HV1 #_ #_ #_ #_ #_ #H #_ destruct /2 width=5/
   ]
-| #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
-| #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
-  lapply (IHV … HL12) -IHV #HV
-  lapply (IHT … HL12) -IHT #HT
+| #p #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2 -IH1
+  elim (snv_inv_gref … H)
+| #a #I #V #T #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
+  elim (snv_inv_bind … H) -H /4 width=4/
+| #V #T #HL0 #HT0 #H #L1 #HL12 destruct
+  elim (snv_inv_appl … H) -H #a #W #W0 #U #l #HV #HT #HVW #HW0 #HTU
   lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
-(*
-  lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
-  lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
-*)
-| #L2 #W #T #U #l #_ #_ #HTU #HUW #IHW #IHT #L1 #HL12
-  lapply (IHW … HL12) -IHW #HW
-  lapply (IHT … HL12) -IHT #HT
+  elim (lsubsv_ssta_trans … HVW … HL12) -HVW #W1 #HVW1 #HW1
+  lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
+  elim (dxprs_lsubsv_aux … IH4 IH3 IH2 IH1 … HL12 … HTU) -IH4 -IH3 -IH2 -HTU // /2 width=1/ #X #HTU #H
+  elim (cprs_inv_abst1 Abst W0 … H) -H #W #U2 #HW0 #HU2 #H destruct
+  lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
+  elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
+  lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU ?) [ /2 width=1/ ] -HTU -HW0
+  /4 width=8 by snv_appl, fw_ygt/ (**) (* auto too slow without trace *)
+| #W #T #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
+  elim (snv_inv_cast … H) -H #U #l #HW #HT #HTU #HUW
   lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
-(*  
-  lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
--HL12 -HWU /2 width=4/
+  elim (lsubsv_ssta_trans … HTU … HL12) -HTU #U0 #HTU0 #HU0
+  lapply (cpcs_trans … HU0 … HUW) -U /4 width=4 by snv_cast, fw_ygt/ (**) (* auto too slow without trace *)
 ]
 qed-.
-*)