X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fsnv_lsstas_lpr.ma;h=2ff0d940ce3f0fe0f7bdef452043c10e2b8ed5c4;hb=f6a6221dcb90a12b04378ca2de86192e0e39f9ab;hp=4237778201174ca1ba0e99d3d034ddbfad52a15b;hpb=d1b944b638846d98dfeb21fa6757e89c609be82a;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma
index 423777820..2ff0d940c 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma
@@ -23,10 +23,10 @@ include "basic_2/dynamic/lsubsv_lsstas.ma".
 (* Properties on sn parallel reduction for local environments ***************)
 
 fact lsstas_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_snv_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_lsstas_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_snv_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_lsstas_cpr_lpr h g G1 L1 T1) →
                          ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_lsstas_cpr_lpr h g G1 L1 T1.
 #h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ]
 [ #k #_ #_ #_ #_ #l1 #l2 #_ #_ #X2 #H2 #X3 #H3 #L2 #_ -IH4 -IH3 -IH2 -IH1
@@ -51,13 +51,13 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   |2,4: * #K0 #V0 #X0 #H #HVX0 #HX0
         lapply (ldrop_mono … H … HLK1) -H -HLK1 #H destruct
   ]
-  [ elim (IH1 … HWl1 … HW0 … HW12 … HK12) -IH1 -HW0 /2 width=1 by fqup_fpbr/ #V2 #HWV2 #HV2
+  [ elim (IH1 … HWl1 … HW0 … HW12 … HK12) -IH1 -HW0 /2 width=1 by fqup_fpbg/ #V2 #HWV2 #HV2
     elim (lift_total V2 0 (i+1))
-    /6 width=11 by fqup_fpbr, cpcs_lift, lsstas_ldec, ex2_intro/
-  | elim (IH1 … HVl1 … HW0 … HV12 … HK12) -IH1 -HVl1 -HW0 -HV12 -HK12 -IH2 /2 width=1 by fqup_fpbr/ #W2 #HVW2 #HW02
+    /6 width=11 by fqup_fpbg, cpcs_lift, lsstas_ldec, ex2_intro/
+  | elim (IH1 … HVl1 … HW0 … HV12 … HK12) -IH1 -HVl1 -HW0 -HV12 -HK12 -IH2 /2 width=1 by fqup_fpbg/ #W2 #HVW2 #HW02
     elim (lift_total W2 0 (i+1))
     /4 width=11 by cpcs_lift, lsstas_ldef, ex2_intro/
-  | elim (IH1 … HVl1 … HW0 … HVX0 … HK12) -IH1 -HVl1 -HW0 -HVX0 -HK12 -IH2 -V2 /2 width=1 by fqup_fpbr/ -l1 #W2 #HXW2 #HW02
+  | elim (IH1 … HVl1 … HW0 … HVX0 … HK12) -IH1 -HVl1 -HW0 -HVX0 -HK12 -IH2 -V2 /2 width=1 by fqup_fpbg/ -l1 #W2 #HXW2 #HW02
     elim (lift_total W2 0 (i+1))
     /3 width=11 by cpcs_lift, lsstas_lift, ex2_intro/
   ]
@@ -69,10 +69,10 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   elim (lsstas_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct
   elim (cpr_inv_bind1 … H3) -H3 *
   [ #V2 #T2 #HV12 #HT12 #H destruct
-    elim (IH1 … Hl1 … HTU1 … HT12 (L2.ⓑ{I}V2)) -IH1 -Hl1 -HTU1 -HT12 /2 width=1 by fqup_fpbr, lpr_pair/ -T1
+    elim (IH1 … Hl1 … HTU1 … HT12 (L2.ⓑ{I}V2)) -IH1 -Hl1 -HTU1 -HT12 /2 width=1 by fqup_fpbg, lpr_pair/ -T1
     /4 width=5 by cpcs_bind2, lpr_cpr_conf, lsstas_bind, ex2_intro/
   | #T3 #HT13 #HXT3 #H1 #H2 destruct
-    elim (IH1 … Hl1 … HTU1 … HT13 (L2.ⓓV1)) -IH1 -Hl1 -HTU1 -HT13 /2 width=1 by fqup_fpbr, lpr_pair/ -T1 -HL12 #U3 #HTU3 #HU13
+    elim (IH1 … Hl1 … HTU1 … HT13 (L2.ⓓV1)) -IH1 -Hl1 -HTU1 -HT13 /2 width=1 by fqup_fpbg, lpr_pair/ -T1 -HL12 #U3 #HTU3 #HU13
     elim (lsstas_inv_lift1 … HTU3 L2 … HXT3) -T3
     /5 width=8 by cpcs_cpr_strap1, cpcs_bind1, cpr_zeta, ldrop_ldrop, ex2_intro/
   ]
@@ -83,7 +83,7 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   elim (cpr_inv_appl1 … H3) -H3 *
   [ #V2 #T2 #HV12 #HT12 #H destruct -a -l0 -W1 -W10 -U10 -HV1 -IH4 -IH3 -IH2
     elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1
-    /4 width=5 by fqup_fpbr, cpcs_flat, lpr_cpr_conf, lsstas_appl, ex2_intro/
+    /4 width=5 by fqup_fpbg, cpcs_flat, lpr_cpr_conf, lsstas_appl, ex2_intro/
   | #b #V2 #W2 #W3 #T2 #T3 #HV12 #HW23 #HT23 #H1 #H2 destruct
     elim (snv_inv_bind … HT1) -HT1 #HW2 #HT2
     lapply (da_inv_bind … Hl1) -Hl1 #Hl1
@@ -92,18 +92,18 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
     lapply (cprs_div … HW10 … HW20) -W0 #HW12
     lapply (ssta_da_conf … HVW1 … Hl0) <minus_plus_m_m #H
     elim (snv_fwd_da … HW2) #l #Hl
-    lapply (IH4 … HV1 … 1 … Hl0 W1 ?) /2 width=1 by fqup_fpbr, ssta_lsstas/ #HW1
+    lapply (IH4 … HV1 … 1 … Hl0 W1 ?) /2 width=1 by fqup_fpbg, ssta_lsstas/ #HW1
     lapply (da_cpcs_aux … IH3 IH2 … H … Hl … HW12) // -H
-    /3 width=5 by fpbr_fpbs_trans, fqup_fpbr, ssta_fpbs/ #H destruct
-    lapply (IH3 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #HV2
-    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbr/ #HV2l
-    elim (IH1 … 1 … Hl0 … W1 … HV12 … HL12) /2 width=1 by fqup_fpbr, ssta_lsstas/ -HVW1 #W4 #H #HW14
+    /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, ssta_fpbs/ #H destruct
+    lapply (IH3 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+    lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2l
+    elim (IH1 … 1 … Hl0 … W1 … HV12 … HL12) /2 width=1 by fqup_fpbg, ssta_lsstas/ -HVW1 #W4 #H #HW14
     lapply (lsstas_inv_SO … H) #HV2W4
     lapply (ssta_da_conf … HV2W4 … HV2l) <minus_plus_m_m #HW4l
-    lapply (IH4 … HV2 … HV2l … H) -H /3 width=5 by fpbr_fpbs_trans, fqup_fpbr, cpr_lpr_fpbs/ #HW4
-    lapply (IH3 … HW23 … HL12) /2 width=1 by fqup_fpbr/ #HW3
-    lapply (IH2 … Hl … HW23 … HL12) /2 width=1 by fqup_fpbr/ #HW3l
-    elim (IH1 … Hl1 … HTU2 … HT23 (L2.ⓛW3)) -HTU2 /2 width=1 by fqup_fpbr, lpr_pair/ #U3 #HTU3 #HU23
+    lapply (IH4 … HV2 … HV2l … H) -H /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/ #HW4
+    lapply (IH3 … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3
+    lapply (IH2 … Hl … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3l
+    elim (IH1 … Hl1 … HTU2 … HT23 (L2.ⓛW3)) -HTU2 /2 width=1 by fqup_fpbg, lpr_pair/ #U3 #HTU3 #HU23
     lapply (cpcs_cpr_strap1 … HW12 … HW23) #H
     lapply (lpr_cpcs_conf … HL12 … H) -H #H
     lapply (cpcs_canc_sn … HW14 H) -H #HW43
@@ -114,20 +114,20 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
       @(cpcs_cpr_strap1 … (ⓐV2.ⓛ{b}W3.U3)) /2 width=1 by cpr_beta/
       /4 width=3 by cpcs_flat, cpcs_bind2, lpr_cpr_conf/
     | -U3
-      @(lsubsv_abbr … l) /3 width=7 by fqup_fpbr/
+      @(lsubsv_abbr … l) /3 width=7 by fqup_fpbg/
       #W #W0 #l0 #Hl0 #HV2W #HW30
       lapply (lsstas_ssta_conf_pos … HV2W4 … HV2W) -HV2W #HW4W
       @(lsstas_cpcs_lpr_aux … IH3 IH2 IH1 … Hl0 … HW4W … Hl0 … HW30 … HW43) //
-      [ /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/
+      [ /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/
       ]
-    | -IH1 -IH3 -IH4 /3 width=9 by fqup_fpbr, lpr_pair/
+    | -IH1 -IH3 -IH4 /3 width=9 by fqup_fpbg, lpr_pair/
     ]
   | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -l0 -W1 -W10 -HV1 -IH4 -IH3 -IH2
     elim (snv_inv_bind … HT1) -HT1 #_ #HT0
     lapply (da_inv_bind … Hl1) -Hl1 #Hl1
     elim (lsstas_inv_bind1 … HTU1) -HTU1 #U0 #HTU0 #H destruct
-    elim (IH1 … Hl1 … HTU0 … HT02 (L2.ⓓW2)) -IH1 -Hl1 -HTU0 /2 width=1 by fqup_fpbr, lpr_pair/ -T0 #U2 #HTU2 #HU02
+    elim (IH1 … Hl1 … HTU0 … HT02 (L2.ⓓW2)) -IH1 -Hl1 -HTU0 /2 width=1 by fqup_fpbg, lpr_pair/ -T0 #U2 #HTU2 #HU02
     lapply (lpr_cpr_conf … HL12 … HV10) -HV10 #HV10
     lapply (lpr_cpr_conf … HL12 … HW02) -L1 #HW02
     lapply (cpcs_bind2 b … HW02 … HU02) -HW02 -HU02 #HU02
@@ -143,10 +143,10 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   elim (cpr_inv_cast1 … H3) -H3
   [ * #U2 #T2 #_ #HT12 #H destruct
     elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1 -HL12
-    /3 width=3 by fqup_fpbr, lsstas_cast, ex2_intro/
+    /3 width=3 by fqup_fpbg, lsstas_cast, ex2_intro/
   | #HT1X3
     elim (IH1 … Hl1 … HTU1 … HT1X3 … HL12) -IH1 -Hl1 -HTU1 -HL12
-    /2 width=3 by fqup_fpbr, ex2_intro/
+    /2 width=3 by fqup_fpbg, ex2_intro/
   ]
 ]
 qed-.