- bug fix in the induction for the closure property

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma
index a9a295a9b4fb7c104899240b26c5501914ed23c5..0b18c9432ddaec627e4e6820de93e971260bf8c5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma
@@ -22,10 +22,10 @@ include "basic_2/dynamic/lsubsv_snv.ma".
 (* Properties on context-free parallel reduction for local environments *****)
 
 fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
-                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_lsstas h g G1 L1 T1) →
-                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_lsstas_cpr_lpr h g G1 L1 T1) →
-                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h g G1 L1 T1) →
-                      (∀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_snv_lsstas h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ ⊃≥[h, g] ⦃G1, L1, T1⦄ → IH_lsstas_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ ⊃≥[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ ⊃≥[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
                       ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_snv_cpr_lpr h g G1 L1 T1.
 #h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ]
 [ #k #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #_ destruct -IH4 -IH3 -IH2 -IH1 -H1
@@ -36,29 +36,29 @@ fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
   lapply (fqup_lref … G1 … HLK1) #HKL
   elim (cpr_inv_lref1 … H2) -H2
-  [ #H destruct -HLK1 /4 width=10 by fqup_fpbg, snv_lref/
+  [ #H destruct -HLK1 /4 width=10 by fqup_fpbr, snv_lref/
   | * #K0 #V0 #W0 #H #HVW0 #W0 -HV12
     lapply (ldrop_mono … H … HLK1) -HLK1 -H #H destruct
-    lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbg, snv_lift/
+    lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbr, snv_lift/
   ]
 | #p #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2 -IH1
   elim (snv_inv_gref … H1)
 | #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2
   elim (snv_inv_bind … H1) -H1 #HV1 #HT1
   elim (cpr_inv_bind1 … H2) -H2 *
-  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=8 by fqup_fpbg, snv_bind, lpr_pair/
+  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=8 by fqup_fpbr, snv_bind, lpr_pair/
   | #T2 #HT12 #HXT2 #H1 #H2 destruct -HV1
-    /4 width=10 by fqup_fpbg, snv_inv_lift, lpr_pair, ldrop_ldrop/
+    /4 width=10 by fqup_fpbr, snv_inv_lift, lpr_pair, ldrop_ldrop/
   ]
 | #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct
   elim (snv_inv_appl … H1) -H1 #a #W10 #W1 #U1 #l0 #HV1 #HT1 #Hl0 #HVW1 #HW10 #HTU1
   elim (cpr_inv_appl1 … H2) -H2 *
   [ #V2 #T2 #HV12 #HT12 #H destruct -IH4
-    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
-    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
-    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #H2l0
-    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HVW1 … HV12 … HL12) -Hl0 -HVW1 -HV12 /2 width=1 by fqup_fpbg/ -HV1 #W2 #HVW2 #HW12
-    elim (cpds_cpr_lpr_aux … IH2 IH3 … HTU1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -HT12 -HTU1 #X #HTU2 #H
+    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #HV2
+    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbr/ #HT2
+    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #H2l0
+    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HVW1 … HV12 … HL12) -Hl0 -HVW1 -HV12 /2 width=1 by fqup_fpbr/ -HV1 #W2 #HVW2 #HW12
+    elim (cpds_cpr_lpr_aux … IH2 IH3 … HTU1 … HT12 … HL12) /2 width=1 by fqup_fpbr/ -HT12 -HTU1 #X #HTU2 #H
     elim (cprs_inv_abst1 … H) -H #W20 #U2 #HW120 #_ #H destruct
     lapply (lpr_cprs_conf … HL12 … HW10) -L1 #HW10
     lapply (cpcs_cprs_strap1 … HW10 … HW120) -W1 #HW120
@@ -70,38 +70,38 @@ fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
     elim (snv_inv_bind … HT1) -HT1 #HW20 #HT20
     elim (cpds_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW230 #_ #H destruct -T30
     lapply (cprs_div … HW10 … HW230) -W30 #HW120
-    lapply (snv_ssta_aux … IH4 … Hl0 … HVW1) /2 width=1 by fqup_fpbg/ #HW10
+    lapply (snv_ssta_aux … IH4 … Hl0 … HVW1) /2 width=1 by fqup_fpbr/ #HW10
     lapply (ssta_da_conf … HVW1 … Hl0) <minus_plus_m_m #HlW10
     elim (snv_fwd_da … HW20) #l #Hl
     lapply (da_cpcs_aux … IH1 IH2 … HlW10 … Hl … HW120) // -HlW10
-    /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, ssta_fpbs/ #H destruct
-    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HlV2
-    lapply (IH2 … Hl … HW202 … HL12) /2 width=1 by fqup_fpbg/ #HlW2
-    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HVW1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #W3 #HV2W3 #HW103
+    /3 width=5 by fpbr_fpbs_trans, fqup_fpbr, ssta_fpbs/ #H destruct
+    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #HlV2
+    lapply (IH2 … Hl … HW202 … HL12) /2 width=1 by fqup_fpbr/ #HlW2
+    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HVW1 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #W3 #HV2W3 #HW103
     lapply (ssta_da_conf … HV2W3 … HlV2) <minus_plus_m_m #HlW3
     lapply (cpcs_cpr_strap1 … HW120 … HW202) -HW120 #HW102
     lapply (lpr_cpcs_conf … HL12 … HW102) -HW102 #HW102
     lapply (cpcs_canc_sn … HW103 … HW102) -W10 #HW32
-    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HV1 #HV2
-    lapply (IH1 … HW202 … HL12) /2 width=1 by fqup_fpbg/ -HW20 #HW2
-    lapply (IH1 … HT20 … HT202 … (L2.ⓛW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -HT20 #HT2
+    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbr/ -HV1 #HV2
+    lapply (IH1 … HW202 … HL12) /2 width=1 by fqup_fpbr/ -HW20 #HW2
+    lapply (IH1 … HT20 … HT202 … (L2.ⓛW2) ?) /2 width=1 by fqup_fpbr, lpr_pair/ -HT20 #HT2
     lapply (snv_ssta_aux … IH4 … HlV2 … HV2W3)
-    /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/ #HW3
+    /3 width=5 by fpbr_fpbs_trans, fqup_fpbr, cpr_lpr_fpbs/ #HW3
     lapply (lsubsv_snv_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /3 width=3 by snv_bind, snv_cast/
-    @(lsubsv_abbr … l) /3 width=7 by fqup_fpbg/ #W #W0 #l0 #Hl0 #HV2W #HW20
+    @(lsubsv_abbr … l) /3 width=7 by fqup_fpbr/ #W #W0 #l0 #Hl0 #HV2W #HW20
     lapply (lsstas_ssta_conf_pos … HV2W3 … HV2W) -HV2W #HW3W
     @(lsstas_cpcs_lpr_aux … IH1 IH2 IH3 … HlW3 … HW3W … HlW2 … HW20 … HW32) //
-    [ /3 width=9 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_ssta_fpbs/
-    | /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/
+    [ /3 width=9 by fpbr_fpbs_trans, fqup_fpbr, cpr_lpr_ssta_fpbs/
+    | /3 width=5 by fpbr_fpbs_trans, fqup_fpbr, cpr_lpr_fpbs/
     ]
   | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -IH4
     elim (snv_inv_bind … HT1) -HT1 #HW0 #HT0
     elim (cpds_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
     elim (lift_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
     lapply (lpr_cprs_conf … HL12 … HW10) -HW10 #HW10
-    elim (cpds_cpr_lpr_aux … IH2 IH3 … HTU0 … HT02 (L2.ⓓW2)) /2 width=1 by fqup_fpbg, lpr_pair/ -HTU0 #X #HTU2 #H
+    elim (cpds_cpr_lpr_aux … IH2 IH3 … HTU0 … HT02 (L2.ⓓW2)) /2 width=1 by fqup_fpbr, lpr_pair/ -HTU0 #X #HTU2 #H
     elim (cprs_inv_abst1 … H) -H #W #U2 #HW1 #_ #H destruct -U3
-    elim (ssta_cpr_lpr_aux … IH3 … HVW1 … HV10 … HL12) /2 width=2 by fqup_fpbg/ -IH3 -HVW1 #X #H1 #H2
+    elim (ssta_cpr_lpr_aux … IH3 … HVW1 … HV10 … HL12) /2 width=2 by fqup_fpbr/ -IH3 -HVW1 #X #H1 #H2
     lapply (cpcs_canc_sn … H2 HW10) -W10 #H2
     elim (lift_total X 0 1) #W20 #H3
     lapply (ssta_lift … H1 (L2.ⓓW2) … HV02 … H3) /2 width=1 by ldrop_ldrop/ -H1 #HVW20
@@ -109,11 +109,11 @@ fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
     lapply (cpcs_cprs_strap1 … HW320 … HW1) -W3 #HW20
     elim (cpcs_inv_cprs … HW20) -HW20 #W3 #HW203 #HW3
     lapply (cpds_cprs_trans … (ⓛ{a}W3.U2) HTU2 ?) /2 width=1 by cprs_bind/ -HW3 -HTU2 #HTU2
-    lapply (IH2 … Hl0 … HV10 … HL12) /2 width=1 by fqup_fpbg/ -IH2 -Hl0 #Hl0
+    lapply (IH2 … Hl0 … HV10 … HL12) /2 width=1 by fqup_fpbr/ -IH2 -Hl0 #Hl0
     lapply (da_lift … Hl0 (L2.ⓓW2) … HV02) /2 width=1 by ldrop_ldrop/ -Hl0 #Hl0
-    lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ -HW0 #HW2
-    lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ -HV1 -HV10 #HV0
-    lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -L1 #HT2
+    lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbr/ -HW0 #HW2
+    lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbr/ -HV1 -HV10 #HV0
+    lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbr, lpr_pair/ -L1 #HT2
     lapply (snv_lift … HV0 (L2.ⓓW2) … HV02) /3 width=7 by snv_bind, snv_appl, ldrop_ldrop/
   ]
 | #W1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4
@@ -121,13 +121,13 @@ fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   elim (cpr_inv_cast1 … H2) -H2
   [ * #W2 #T2 #HW12 #HT12 #H destruct
     lapply (cpcs_cprs_strap1 … HUW1 W2 ?) /2 width=1 by cpr_cprs/ -HUW1 #H1
-    lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbg/ -HW1 -HW12 #HW2
-    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -IH1 #HT2
-    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HTU1 … HT12 … HL12) /2 width=2 by fqup_fpbg/ -IH3 -HTU1 #U2 #HTU2 #HU12
-    lapply (IH2 … Hl0 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -IH2 -HT1 -HT12 -Hl0 #Hl0
+    lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbr/ -HW1 -HW12 #HW2
+    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbr/ -IH1 #HT2
+    elim (ssta_cpr_lpr_aux … IH3 … Hl0 … HTU1 … HT12 … HL12) /2 width=2 by fqup_fpbr/ -IH3 -HTU1 #U2 #HTU2 #HU12
+    lapply (IH2 … Hl0 … HT12 … HL12) /2 width=1 by fqup_fpbr/ -IH2 -HT1 -HT12 -Hl0 #Hl0
     /4 width=7 by snv_cast, lpr_cpcs_conf, cpcs_canc_sn/
   | #H -IH3 -IH2 -HW1 -HTU1 -HUW1
-    lapply (IH1 … H … HL12) /2 width=1 by fqup_fpbg/
+    lapply (IH1 … H … HL12) /2 width=1 by fqup_fpbr/
   ]
 ]
 qed-.