- advances in the theory of cofrees

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

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 5166e92a22cc8febc8bfad6bd170966720015bbf..1ee5ba08ec4cf80bfefd4f3e092a91f8d8b63484 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lsstas_lpr.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "basic_2/computation/cpds_cpds.ma".
-include "basic_2/computation/fpbs_fpbs.ma".
 include "basic_2/dynamic/snv_aaa.ma".
 include "basic_2/dynamic/snv_cpcs.ma".
 include "basic_2/dynamic/lsubsv_lsstas.ma".
@@ -23,10 +22,10 @@ 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
@@ -45,7 +44,7 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   lapply (fqup_lref … G1 … HLK1) #HKV1
   elim (lpr_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
   elim (lpr_inv_pair1 … H) -H #K2 [ #W2 | #V2 ] #HK12 [ #HW12 | #HV12 ] #H destruct
-  lapply (ldrop_fwd_ldrop2 … HLK2) #H2
+  lapply (ldrop_fwd_drop2 … HLK2) #H2
   elim (cpr_inv_lref1 … H3) -H3
   [1,3: #H destruct -HLK1
   |2,4: * #K0 #V0 #X0 #H #HVX0 #HX0
@@ -53,13 +52,13 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   ]
   [ 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_fpbg, cpcs_lift, lsstas_ldec, ex2_intro/
+    /6 width=12 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/
+    /4 width=12 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_fpbg/ -l1 #W2 #HXW2 #HW02
     elim (lift_total W2 0 (i+1))
-    /3 width=11 by cpcs_lift, lsstas_lift, ex2_intro/
+    /3 width=12 by cpcs_lift, lsstas_lift, ex2_intro/
   ]
 | #p #_ #_ #HT0 #H1 destruct -IH4 -IH3 -IH2 -IH1
   elim (snv_inv_gref … H1)
@@ -74,7 +73,7 @@ fact lsstas_cpr_lpr_aux: ∀h,g,G0,L0,T0.
   | #T3 #HT13 #HXT3 #H1 #H2 destruct
     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/
+    /5 width=8 by cpcs_cpr_strap1, cpcs_bind1, cpr_zeta, ldrop_drop, ex2_intro/
   ]
 | #V1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 #Hl21 #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct
   elim (snv_inv_appl … H1) -H1 #a #W1 #W10 #U10 #l0 #HV1 #HT1 #Hl0 #HVW1 #HW10 #HTU10