lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma
index e40d8a2824e4e3ee92fa6d764a3dadf8da4b1a1d..eb698c599b570e0d175fd5205f167042070cf60a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/dxprs_lift.ma".
+include "basic_2/computation/cpds_lift.ma".
 include "basic_2/equivalence/cpcs_cpcs.ma".
 include "basic_2/dynamic/snv.ma".
 
@@ -27,8 +27,8 @@ lemma snv_lift: ∀h,g,K,T. ⦃h, K⦄ ⊢ T ¡[g] → ∀L,d,e. ⇩[d, e] L ≡
   >(lift_inv_sort1 … H) -X -K -d -e //
 | #I #K #K0 #V #i #HK0 #_ #IHV #L #d #e #HLK #X #H
   elim (lift_inv_lref1 … H) * #Hid #H destruct
-  [ elim (ldrop_trans_le … HLK … HK0 ?) -K /2 width=2/ #X #HL0 #H
-    elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #L0 #W #HLK0 #HVW #H destruct
+  [ elim (ldrop_trans_le … HLK … HK0) -K /2 width=2/ #X #HL0 #H
+    elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #L0 #W #HLK0 #HVW #H destruct
     /3 width=8/
   | lapply (ldrop_trans_ge … HLK … HK0 ?) -K // -Hid /3 width=8/
   ]
@@ -42,7 +42,7 @@ lemma snv_lift: ∀h,g,K,T. ⦃h, K⦄ ⊢ T ¡[g] → ∀L,d,e. ⇩[d, e] L ≡
   elim (lift_total T1 (d+1) e) #U1 #HTU1
   @(snv_appl … a … W0 … W1 … U1 l)
   [ /2 width=4/ | /2 width=4/ | /2 width=9/ | /2 width=9/ ]
-  @(dxprs_lift … HLK … HTU … HT1) /2 width=1/
+  @(cpds_lift … HLK … HTU … HT1) /2 width=1/
 | #K #V0 #T #V #l #_ #_ #HTV #HV0 #IHV0 #IHT #L #d #e #HLK #X #H
   elim (lift_inv_flat1 … H) -H #W0 #U #HVW0 #HTU #H destruct
   elim (lift_total V d e) #W #HVW
@@ -57,8 +57,8 @@ lemma snv_inv_lift: ∀h,g,L,U. ⦃h, L⦄ ⊢ U ¡[g] → ∀K,d,e. ⇩[d, e] L
   >(lift_inv_sort2 … H) -X -L -d -e //
 | #I #L #L0 #W #i #HL0 #_ #IHW #K #d #e #HLK #X #H
   elim (lift_inv_lref2 … H) * #Hid #H destruct
-  [ elim (ldrop_conf_le … HLK … HL0 ?) -L /2 width=2/ #X #HK0 #H
-    elim (ldrop_inv_skip1 … H ?) -H /2 width=1/ -Hid #K0 #V #HLK0 #HVW #H destruct
+  [ elim (ldrop_conf_le … HLK … HL0) -L /2 width=2/ #X #HK0 #H
+    elim (ldrop_inv_skip1 … H) -H /2 width=1/ -Hid #K0 #V #HLK0 #HVW #H destruct
     /3 width=8/
   | lapply (ldrop_conf_ge … HLK … HL0 ?) -L // -Hid /3 width=8/
   ]
@@ -67,8 +67,8 @@ lemma snv_inv_lift: ∀h,g,L,U. ⦃h, L⦄ ⊢ U ¡[g] → ∀K,d,e. ⇩[d, e] L
 | #a #L #W #W0 #W1 #U #U1 #l #_ #_ #HW0 #HW01 #HU1 #IHW #IHU #K #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #V #T #HVW #HTU #H destruct
   elim (ssta_inv_lift1 … HW0 … HLK … HVW) -HW0 #V0 #HV0 #HVW0
-  elim (cprs_inv_lift1 … HLK … HVW0 … HW01) -W0 #V1 #HVW1 #HV01
-  elim (dxprs_inv_lift1 … HLK … HTU … HU1) -HU1 #X #H #HTU
+  elim (cprs_inv_lift1 … HW01 … HLK … HVW0) -W0 #V1 #HVW1 #HV01
+  elim (cpds_inv_lift1 … HLK … HTU … HU1) -HU1 #X #H #HTU
   elim (lift_inv_bind2 … H) -H #Y #T1 #HY #HTU1 #H destruct
   lapply (lift_inj … HY … HVW1) -HY #H destruct /3 width=8/
 | #L #W0 #U #W #l #_ #_ #HUW #HW0 #IHW0 #IHU #K #d #e #HLK #X #H
@@ -85,12 +85,14 @@ lemma snv_fsup_conf: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
 #h #g #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2
 [ #I1 #L1 #V1 #H
   elim (snv_inv_lref … H) -H #I2 #L2 #V2 #H #HV2
-  lapply (ldrop_inv_refl … H) -H #H destruct //
-|2,3: #a #I #L1 #V1 #T1 #H elim (snv_inv_bind … H) -H //
-|4,5: * #L1 #V1 #T1 #H
+  lapply (ldrop_inv_O2 … H) -H #H destruct //
+|2: *
+|5,6: /3 width=7 by snv_inv_lift/
+]
+[1,3: #a #I #L1 #V1 #T1 #H elim (snv_inv_bind … H) -H //
+|2,4: * #L1 #V1 #T1 #H
   [1,3: elim (snv_inv_appl … H) -H //
   |2,4: elim (snv_inv_cast … H) -H //
   ]
-| /3 width=7 by snv_inv_lift/
 ]
 qed-.