lambdadelta

[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 db1058f758e58a144e4e6cda0bb11972223444f4..39a60a97a495f4c7991c27548d5c707722279b97 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpr.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/dxprs_dxprs.ma".
+include "basic_2/computation/cpds_cpds.ma".
 include "basic_2/dynamic/snv_lift.ma".
 include "basic_2/dynamic/snv_cpcs.ma".
 
@@ -61,33 +61,34 @@ fact snv_cpr_lpr_aux: ∀h,g,L0,T0.
     lapply (IH1 … HV1 … HV12 … HL12) [ /2 width=1/ ] #HV2
     lapply (IH1 … HT1 … HT12 … HL12) [ /2 width=1/ ] #HT2
     elim (IH3 … HVW1 … HV12 … HL12) -HVW1 -HV12 // -HV1 [2: /2 width=1/ ] #W2 #HVW2 #HW12
-    elim (dxprs_cprs_lpr_aux … IH2 IH1 IH3 … HTU1 … T2 … HL12) // [2,3: /2 width=1/ ] -IH2 -IH1 -IH3 -HT1 -HT12 -HTU1 #X #HTU2 #H
-    elim (cprs_fwd_abst1 … H Abst W1) -H #W20 #U2 #HW120 #_ #H destruct
-    lapply (cprs_lpr_conf … HL12 … HW10) -L1 #HW10
+    elim (cpds_cprs_lpr_aux … IH2 IH1 IH3 … HTU1 … T2 … HL12) // [2,3: /2 width=1/ ] -IH2 -IH1 -IH3 -HT1 -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
     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 -HTU2 /2 width=8/
-  | #b #V2 #W20 #T20 #T2 #HV12 #HT202 #H1 #H2 destruct
+    lapply (cpds_cprs_trans … (ⓛ{a}W0.U2) HTU2 ?) [ /2 width=1/ ] -HW200 -HTU2 /2 width=8/
+  | #b #V2 #W20 #W2 #T20 #T2 #HV12 #HW202 #HT202 #H1 #H2 destruct
     elim (snv_inv_bind … HT1) -HT1 #HW20 #HT20
-    elim (dxprs_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW230 #_ #H destruct -T30
+    elim (cpds_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW230 #_ #H destruct -T30
     lapply (cprs_div … HW10 … HW230) -W30 #HW120
-    lapply (cpcs_lpr_conf … HL12 … HW120) -HW120 #HW120
-    elim (IH3 … HVW1 … HV12 … HL12) // [2: /2 width=1/ ] -HVW1 #W2 #HVW2 #HW102
-    lapply (cpcs_canc_sn … HW102 … HW120) -W10 #HW220
-    lapply (IH1 … HV12 … HL12) // [ /2 width=1/ ] #HV2 -HV1
-    lapply (IH1 … HW20 … W20 … HL12) // [ /2 width=1/ ] -HW20 #HW20
-    lapply (IH1 … HT20 … HT202 … (L2.ⓛW20) ?) [1,2: /2 width=1/ ] -HT20 #HT2
-    lapply (IH2 … HVW2) //
+    lapply (cpcs_cpr_strap1 … HW120 … HW202) -HW120 #HW102
+    lapply (lpr_cpcs_conf … HL12 … HW102) -HW102 #HW102
+    elim (IH3 … HVW1 … HV12 … HL12) // [2: /2 width=1/ ] -HVW1 #W3 #HV2W3 #HW103
+    lapply (cpcs_canc_sn … HW103 … HW102) -W10 #HW32
+    lapply (IH1 … HV12 … HL12) // [ /2 width=1/ ] -HV1 #HV2
+    lapply (IH1 … HW202 … HL12) // [ /2 width=1/ ] -HW20 #HW2
+    lapply (IH1 … HT20 … HT202 … (L2.ⓛW2) ?) [1,2: /2 width=1/ ] -HT20 #HT2
+    lapply (IH2 … HV2W3) //
     [ @(ygt_yprs_trans … L1 L1 … V1) (**) (* auto /4 width=5/ is a bit slow even with trace *)
       [ /2 width=1 by fsupp_ygt/
       | /3 width=1 by cprs_lpr_yprs, cpr_cprs/
       ]
-    ] #HW2
-    elim (snv_fwd_ssta … HW20) #l0 #U20 #HWU20
-    elim (ssta_fwd_correct … HVW2) <minus_plus_m_m #U2 #HWU2
-    elim (ssta_cpcs_lpr_aux … IH1 IH3 … HWU2 … HWU20 … HW220 … L2) // -IH3
-    [2: /4 width=4 by ygt_yprs_trans, fsupp_ygt, ypr_yprs, ypr_lpr/
+    ] #HW3
+    elim (snv_fwd_ssta … HW2) #l0 #U2 #HWU2
+    elim (ssta_fwd_correct … HV2W3) <minus_plus_m_m #U3 #HWU3
+    elim (ssta_cpcs_lpr_aux … IH1 IH3 … HWU3 … HWU2 … HW32 … L2) // -IH3
+    [2: /4 width=5 by ygt_yprs_trans, fsupp_ygt, cprs_lpr_yprs, cpr_cprs/
     |3: @(ygt_yprs_trans … L1 L2 … V2) (**) (* auto not tried *)
         [ @(ygt_yprs_trans … L1 L1 … V1)
           [ /2 width=1 by fsupp_ygt/
@@ -95,21 +96,21 @@ fact snv_cpr_lpr_aux: ∀h,g,L0,T0.
           ]
         | /3 width=2 by ypr_ssta, ypr_yprs/
         ]
-    ] #H #_  destruct -IH2 -U2
-    lapply (IH4 … HT2 (L2.ⓓV2) ?)
-    [ /2 width=6/
+    ] #H #_  destruct -IH2 -U3
+    lapply (IH4 … HT2 (L2.ⓓⓝW2.V2) ?)
+    [ /3 width=5/
     | @(ygt_yprs_trans … (L1.ⓛW20) … T2) (**) (* auto /5 width=5/ is too slow even with trace timeout=35 *)
       [ /4 width=4 by ygt_yprs_trans, fsupp_ygt, ypr_yprs, ypr_cpr/
       | /4 width=1 by ypr_yprs, ypr_lpr, lpr_pair/
       ]
-    ] -L1 -V1 -W2 -T20 -U20 -W20 -l0 /2 width=1/
+    ] -L1 -V1 -T20 -U2 /3 width=4/
   | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #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 (cpds_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
     elim (lift_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
-    lapply (cprs_lpr_conf … HL12 … HW10) -HW10 #HW10
-    elim (dxprs_cprs_lpr_aux … IH2 IH1 IH3 … HTU0 T2 … (L2.ⓓW2) ?) // [2,3,4: /2 width=1/ ] -IH2 -HTU0 #X #HTU2 #H
-    elim (cprs_fwd_abst1 … H Abst W3) -H #W #U2 #HW1 #_ #H destruct -U3
+    lapply (lpr_cprs_conf … HL12 … HW10) -HW10 #HW10
+    elim (cpds_cprs_lpr_aux … IH2 IH1 IH3 … HTU0 T2 … (L2.ⓓW2)) // [2,3,4: /2 width=1/ ] -IH2 -HTU0 #X #HTU2 #H
+    elim (cprs_inv_abst1 … H) -H #W #U2 #HW1 #_ #H destruct -U3
     elim (IH3 … HVW1 … HV10 … HL12) // /2 width=1/ -IH3 -HVW1 #X #H1 #H2
     lapply (cpcs_canc_sn … H2 HW10) -W10 #H2
     elim (lift_total X 0 1) #W20 #H3
@@ -117,7 +118,7 @@ fact snv_cpr_lpr_aux: ∀h,g,L0,T0.
     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 (cpds_cprs_trans … (ⓛ{a}W3.U2) HTU2 ?) [ /2 width=1/ ] -HW3 -HTU2 #HTU2
     lapply (IH1 … HW02 … HL12) // [ /2 width=1/ ] -HW0 #HW2
     lapply (IH1 … HV10 … HL12) // [ /2 width=1/ ] -HV1 -HV10 #HV0
     lapply (IH1 … HT02 (L2.ⓓW2) ?) // [1,2: /2 width=1/ ] -L1 #HT2
@@ -131,7 +132,7 @@ fact snv_cpr_lpr_aux: ∀h,g,L0,T0.
     lapply (IH1 … HW12 … HL12) // /2 width=1/ -HW1 -HW12 #HW2
     lapply (IH1 … HT12 … HL12) // /2 width=1/ -IH1 #HT2
     elim (IH3 … HTU1 … HT12 … HL12) // /2 width=1/ -IH3 -HT1 -HT12 -HTU1 #U2 #HTU2 #HU12
-    lapply (cpcs_lpr_conf … HL12 … H1) -L1 #H1
+    lapply (lpr_cpcs_conf … HL12 … H1) -L1 #H1
     lapply (cpcs_canc_sn … HU12 H1) -U1 /2 width=4/
   | #H -IH3 -HW1 -HTU1 -HUW1
     lapply (IH1 … H … HL12) // /2 width=1/