update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
index f3238fbd9cc57fae42cc247c2c740a493714f102..6a0be595354bbd493f49bb797b84069551fc2c51 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
@@ -41,7 +41,7 @@ fact snv_ltpr_tpr_aux: ∀h,g,L0,T0.
   elim (snv_inv_bind … H1) -H1 #HV1 #HT1
   elim (tpr_inv_bind1 … H2) -H2 *
   [ #V2 #T0 #T2 #HV12 #HT10 #HT02 #H destruct
-    lapply (tps_lsubs_trans … HT02 (L2.ⓑ{I}V2) ?) -HT02 /2 width=1/ #HT02
+    lapply (tps_lsubr_trans … HT02 (L2.ⓑ{I}V2) ?) -HT02 /2 width=1/ #HT02
     lapply (IH1 … HL12 … HV12) // [ /2 width=1/ ] #HV2
     lapply (snv_ltpr_cpr_aux … HT1  (L2.ⓑ{I}V2) … T2 ?) -HT1
     [ /3 width=5 by cpr_intro, tps_tpss/ | /2 width=1/ | /3 width=1/ ] -IH1 -T0 /2 width=1/
@@ -62,19 +62,52 @@ fact snv_ltpr_tpr_aux: ∀h,g,L0,T0.
     lapply (cpcs_cprs_strap1 … HW10 … HW120) -W1 #HW120
     lapply (cpcs_canc_sn … HW12 HW120) -W10 #HW20
     elim (cpcs_inv_cprs … HW20) -HW20 #W0 #HW20 #HW200
-    lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU2 ?) [ /2 width=1/ ] -HW200 /2 width=8/
+    lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU2 ?) [ /2 width=1/ ] -HW200 -HTU2 /2 width=8/
   | #b #V2 #W20 #T20 #T2 #HV12 #HT202 #H1 #H2 destruct
     elim (snv_inv_bind … HT1) -HT1 #HW20 #HT20
     elim (dxprs_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW230 #_ #H destruct -T30
-    lapply (cprs_div … HW230 … HW10) -W30 #HW210
-    lapply (ltpr_cpcs_conf … HL12 … HW210) -HW210 #HW210
+    lapply (cprs_div … HW10 … HW230) -W30 #HW120
+    elim (snv_fwd_ssta … HW20) #l0 #U20 #HWU20
+    elim (ssta_fwd_correct … HVW1) <minus_plus_m_m #U10 #HWU10
+    elim (ssta_ltpr_cpcs_aux … IH1 IH3 … HW20 … HWU10 … HWU20) // -IH3 -HWU10
+    [2: /3 width=5/ |3: /2 width=1/
+    |4: /4 width=4 by ygt_yprs_trans, fw_ygt, sstas_yprs, ssta_sstas/
+    ] #H #_ -IH2 -U10 destruct
+    lapply (IH4 … HT20 (L1.ⓓV1) ?) [ /2 width=6/ | /2 width=1/ ] -U20 -W10 -l0 -IH4 -HT20 -HW20 #HT20
     lapply (IH1 … HL12 … HV12) // [ /2 width=1/ ] #HV2
-    lapply (IH1 … HW20 … HL12 W20 ?) // [ /2 width=1/ ] -HW20 #HW20
-    lapply (IH1 … HT20 … (L2.ⓛW20) … HT202) [1,2: /2 width=1/ ] -IH1 -HT20 -HT202 #HT2
-    elim (IH3 … HVW1 … HL12 … HV12) // [2: /2 width=1/ ] -HV1 -HVW1 -HV12 #W200 #HVW200 #H
-    lapply (cpcs_trans … HW210 … H) -W10 #HW200
-    lapply (IH4 … HT2 (L2.ⓓV2) ?) -HT2
-    [ (* /2 width=4/ *)
-    |
-    | /2 width=1/
-    ] 
+    lapply (IH1 … HT20 … (L2.ⓓV2) … HT202) [1,2: /2 width=1/ ] -L1 -V1 -W20 -T20 /2 width=1/
+  | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HW02 #HT02 #HV02 #H1 #H2 destruct -IH4
+    elim (snv_inv_bind … HT1) -HT1 #HW0 #HT0
+    elim (dxprs_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
+    elim (lift_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
+    lapply (ltpr_cprs_conf … HL12 … HW10) -HW10 #HW10
+    elim (dxprs_ltpr_cprs_aux … IH2 IH1 IH3 … HTU0 (L2.ⓓW2) … T2 ?) // [2: /3 width=1/ |3,4: /2 width=1/ ] -IH2 -HTU0 #X #HTU2 #H
+    elim (cprs_inv_abst1 Abst W3 … H) -H #W #U2 #HW1 #_ #H destruct -U3
+    elim (IH3 … HVW1 … HL12 … HV10) // /2 width=1/ -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/ -H1 #HVW20
+    lapply (cpcs_lift (L2.ⓓW2) … H3 … HW13 H2) /2 width=1/ -HW13 -H3 -H2 #HW320
+    lapply (cpcs_cprs_strap1 … HW320 … HW1) -W3 #HW20
+    elim (cpcs_inv_cprs … HW20) -HW20 #W3 #HW203 #HW3
+    lapply (dxprs_cprs_trans … (ⓛ{a}W3.U2) HTU2 ?) [ /2 width=1/ ] -HW3 -HTU2 #HTU2
+    lapply (IH1 … HL12 … HW02) // [ /2 width=1/ ] -HW0 #HW2
+    lapply (IH1 … HL12 … HV10) // [ /2 width=1/ ] -HV1 -HV10 #HV0
+    lapply (IH1 … HT0 … (L2.ⓓW2) … HT02) [1,2: /2 width=1/ ] -L1 -HT02 -HW02 #HT2
+    lapply (snv_lift … HV0 (L2.ⓓW2) … HV02) /2 width=1/ -HV0 -HV02 /3 width=8/
+  ]
+| #W1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH4 -IH2
+  elim (snv_inv_cast … H1) -H1 #U1 #l #HW1 #HT1 #HTU1 #HUW1
+  elim (tpr_inv_cast1 … H2) -H2
+  [ * #W2 #T2 #HW12 #HT12 #H destruct
+    lapply (cpcs_cprs_strap1 … HUW1 W2 ?) [ /3 width=1/ ] -HUW1 #H1
+    lapply (IH1 … HL12 … HW12) // /2 width=1/ -HW1 -HW12 #HW2
+    lapply (IH1 … HL12 … HT12) // /2 width=1/ -IH1 #HT2
+    elim (IH3 … HTU1 … HL12 … HT12) // /2 width=1/ -IH3 -HT1 -HT12 -HTU1 #U2 #HTU2 #HU12
+    lapply (ltpr_cpcs_conf … HL12 … H1) -L1 #H1
+    lapply (cpcs_canc_sn … HU12 H1) -U1 /2 width=4/
+  | #H -IH3 -HW1 -HTU1 -HUW1
+    lapply (IH1 … HL12 … H) // /2 width=1/
+  ]
+]  
+qed-.