preservation of stratified vaildity through ordinary reduction and static typing

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsstas.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsstas.ma
index 500d2f6879707b1b8dfaa5449b76c127fc97532e..ec2ae57bc94c5af752012601632d16325e72b17f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsstas.ma
@@ -24,10 +24,10 @@ include "basic_2/dynamic/lsubsv_lsubd.ma".
 
 lemma lsubsv_lsstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, g, l1] U2 →
                            ∀l2. l1 ≤ l2 → ⦃G, L2⦄ ⊢ T ▪[h, g] l2 →
-                           â\88\80L1. G â\8a¢ L1 ¡â\8a\91[h, g] L2 →
+                           â\88\80L1. G â\8a¢ L1 ¡â«\83[h, g] L2 →
                            ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, g, l1] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
 #h #g #G #L2 #T #U #l1 #H @(lsstas_ind_alt … H) -G -L2 -T -U -l1
-[1,2: /2 width=3/
+[1,2: /2 width=3 by lstar_O, ex2_intro/
 | #G #L2 #K2 #X #Y #U #i #l1 #HLK2 #_ #HYU #IHXY #l2 #Hl12 #Hl2 #L1 #HL12
   elim (da_inv_lref … Hl2) -Hl2 * #K0 #V0 [| #l0 ] #HK0 #HV0
   lapply (ldrop_mono … HK0 … HLK2) -HK0 #H destruct
@@ -35,9 +35,9 @@ lemma lsubsv_lsstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, g, l1]
   elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HYU -IHXY -HLK1 ]
   [ #HK12 #H destruct
     elim (IHXY … Hl12 HV0 … HK12) -K2 -l2 #T #HXT #HTY
-    lapply (ldrop_fwd_ldrop2 … HLK1) #H
+    lapply (ldrop_fwd_drop2 … HLK1) #H
     elim (lift_total T 0 (i+1))
-    /3 width=11 by lsstas_ldef, cpcs_lift, ex2_intro/
+    /3 width=12 by lsstas_ldef, cpcs_lift, ex2_intro/
   | #V #l0 #_ #_ #_ #_ #_ #_ #_ #H destruct
   ]
 | #G #L2 #K2 #X #Y #U #i #l1 #l #HLK2 #_ #_ #HYU #IHXY #l2 #Hl12 #Hl2 #L1 #HL12 -l
@@ -50,9 +50,9 @@ lemma lsubsv_lsstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, g, l1]
     lapply (lsubsv_fwd_lsubd … HK12) #H
     lapply (lsubd_da_trans … HV0 … H) -H
     elim (IHXY … Hl12 HV0 … HK12) -K2 -Hl12 #Y0
-    lapply (ldrop_fwd_ldrop2 … HLK1)
+    lapply (ldrop_fwd_drop2 … HLK1)
     elim (lift_total Y0 0 (i+1))
-    /3 width=11 by lsstas_ldec, cpcs_lift, ex2_intro/
+    /3 width=12 by lsstas_ldec, cpcs_lift, ex2_intro/
   | #V #l #_ #_ #HVX #_ #HV #HX #HK12 #_ #H destruct
     lapply (da_mono … HX … HV0) -HX #H destruct
     elim (IHXY … Hl12 HV0 … HK12) -K2 #Y0 #HXY0 #HY0
@@ -60,9 +60,9 @@ lemma lsubsv_lsstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, g, l1]
     elim (lsstas_total … HVW (l1+1)) -W #W #HVW
     lapply (HVX … Hl12 HVW HXY0) -HVX -Hl12 -HXY0 #HWY0
     lapply (cpcs_trans … HWY0 … HY0) -Y0
-    lapply (ldrop_fwd_ldrop2 … HLK1)
+    lapply (ldrop_fwd_drop2 … HLK1)
     elim (lift_total W 0 (i+1))
-    /4 width=11 by lsstas_ldef, lsstas_cast, cpcs_lift, ex2_intro/
+    /4 width=12 by lsstas_ldef, lsstas_cast, cpcs_lift, ex2_intro/
   ]
 | #a #I #G #L2 #V2 #T2 #U2 #l1 #_ #IHTU2 #l2 #Hl12 #Hl2 #L1 #HL12
   lapply (da_inv_bind … Hl2) -Hl2 #Hl2
@@ -81,7 +81,7 @@ qed-.
 
 lemma lsubsv_ssta_trans: ∀h,g,G,L2,T,U2. ⦃G, L2⦄ ⊢ T •[h, g] U2 →
                          ∀l. ⦃G, L2⦄ ⊢ T ▪[h, g] l+1 →
-                         â\88\80L1. G â\8a¢ L1 ¡â\8a\91[h, g] L2 →
+                         â\88\80L1. G â\8a¢ L1 ¡â«\83[h, g] L2 →
                          ∃∃U1. ⦃G, L1⦄ ⊢ T •[h, g] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
 #h #g #G #L2 #T #U2 #H #l #HTl #L1 #HL12
 elim ( lsubsv_lsstas_trans … U2 1 … HTl … HL12)