- degree assignment, static type assignment, iterated static type

[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 840e4a31aa7529676874a15e8fec6ead0dea5fd1..dcf7b73478858d26ccc6f070ccde0e283a67de89 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.ma
@@ -13,6 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/computation/cpds_cpds.ma".
+include "basic_2/dynamic/snv_aaa.ma".
 include "basic_2/dynamic/lsubsv_cpds.ma".
 include "basic_2/dynamic/lsubsv_cpcs.ma".
 
@@ -20,40 +21,32 @@ include "basic_2/dynamic/lsubsv_cpcs.ma".
 
 (* Properties concerning stratified native validity *************************)
 
-fact snv_lsubsv_aux: ∀h,g,G0,L0,T0.
-                     (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
-                     (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_ssta_cpr_lpr h g G1 L1 T1) →
-                     (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_ssta h g G1 L1 T1) →
-                     (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_lsubsv h g G1 L1 T1) →
-                     ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_snv_lsubsv h g G1 L1 T1.
-#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G #L2 * * [||||*] //
-[ #i #HG0 #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
+lemma lsubsv_snv_trans: ∀h,g,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, g] →
+                        ∀L1. G ⊢ L1 ¡⊑[h, g] L2 → ⦃G, L1⦄ ⊢ T ¡[h, g].
+#h #g #G #L2 #T #H elim H -G -L2 -T //
+[ #I #G #L2 #K2 #V #i #HLK2 #_ #IHV #L1 #HL12
+  elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
   elim (lsubsv_inv_pair2 … H) -H * #K1
-  [ #HK12 #H destruct
-    /5 width=8 by snv_lref, fsupp_ygt, fsupp_lref/ (**) (* auto too slow without trace *)
-  | #V #W1 #V2 #l #HV #_ #_ #_ #_ #_ #H destruct /2 width=5/
+  [ #HK12 #H destruct /3 width=5 by snv_lref/
+  | #W #l #H1V #H1W #HWV #_ #HWl #_ #_ #H1 #H2 destruct -IHV
+    /3 width=10 by snv_scast, snv_lref/
   ]
-| #p #HG0 #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2 -IH1
-  elim (snv_inv_gref … H)
-| #a #I #V #T #HG0 #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
-  elim (snv_inv_bind … H) -H /4 width=4/
-| #V #T #HG0 #HL0 #HT0 #H #L1 #HL12 destruct
-  elim (snv_inv_appl … H) -H #a #W #W0 #U #l #HV #HT #HVW #HW0 #HTU
+| #a #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 destruct
+  /4 width=1 by snv_bind, lsubsv_pair/
+| #a #G #L2 #V #W #W0 #T #U #l #_ #_ #HVl #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
   lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
-  elim (lsubsv_ssta_trans … HVW … HL12) -HVW #W1 #HVW1 #HW1
+  elim (lsubsv_ssta_trans … HVW … HVl … HL12) -HVW #W1 #HVW1 #HW1
   lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
-  elim (lsubsv_cpds_aux … IH4 IH3 IH2 IH1 … HL12 … HTU) -IH4 -IH3 -IH2 -HTU // /2 width=1/ #X #HTU #H
-  elim (cprs_inv_abst1 … H) -H #W #U2 #HW0 #HU2 #H destruct
+  lapply (lsubd_da_trans … HVl L1 ?) -HVl /2 width=1 by lsubsv_fwd_lsubd/ #HVl
+  elim (lsubsv_cpds_trans … HTU … HL12) -HTU #X #HTU #H
+  elim (cprs_inv_abst1 … H) -H #W #U2 #HW0 #_ #H destruct
   lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
   elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
-  lapply (cpds_cprs_trans … (ⓛ{a}W0.U2) HTU ?) [ /2 width=1/ ] -HTU -HW0
-  /4 width=8 by snv_appl, fsupp_ygt/ (**) (* auto too slow without trace *)
-| #W #T #HG0 #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
-  elim (snv_inv_cast … H) -H #U #l #HW #HT #HTU #HUW
+  /4 width=11 by snv_appl, cpds_cprs_trans, cprs_bind/
+| #G #L2 #W #T #U #l #_ #_ #HTl #HTU #HUW #IHW #IHT #L1 #HL12
   lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
-  elim (lsubsv_ssta_trans … HTU … HL12) -HTU #U0 #HTU0 #HU0
-  lapply (cpcs_trans … HU0 … HUW) -U /4 width=4 by snv_cast, fsupp_ygt/ (**) (* auto too slow without trace *)
+  elim (lsubsv_ssta_trans … HTU … HTl … HL12) -HTU #U0 #HTU0 #HU0
+  lapply (lsubd_da_trans … HTl L1 ?) -HTl
+  /4 width=5 by lsubsv_fwd_lsubd, snv_cast, cpcs_trans/
 ]
 qed-.