commit completed: now we support two versions of slicing for local

[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 bb7ac6ca55db0b274ca15dd09879b62b2bf14412..b865349845f0e02500e2a01a9426e564ce3df4ff 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma
@@ -20,63 +20,67 @@ include "basic_2/dynamic/snv.ma".
 
 (* Relocation properties ****************************************************)
 
-lemma snv_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ T ¡[h, g] → ∀L,d,e. ⇩[d, e] L ≡ K →
+lemma snv_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ T ¡[h, g] → ∀L,s,d,e. ⇩[s, d, e] L ≡ K →
                 ∀U. ⇧[d, e] T ≡ U → ⦃G, L⦄ ⊢ U ¡[h, g].
 #h #g #G #K #T #H elim H -G -K -T
-[ #G #K #k #L #d #e #_ #X #H
+[ #G #K #k #L #s #d #e #_ #X #H
   >(lift_inv_sort1 … H) -X -K -d -e //
-| #I #G #K #K0 #V #i #HK0 #_ #IHV #L #d #e #HLK #X #H
+| #I #G #K #K0 #V #i #HK0 #_ #IHV #L #s #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
-    /3 width=8/
-  | lapply (ldrop_trans_ge … HLK … HK0 ?) -K // -Hid /3 width=8/
+  [ elim (ldrop_trans_le … HLK … HK0) -K /2 width=2 by lt_to_le/ #X #HL0 #H
+    elim (ldrop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid #L0 #W #HLK0 #HVW #H destruct
+    /3 width=9 by snv_lref/
+  | lapply (ldrop_trans_ge … HLK … HK0 ?) -K
+    /3 width=9 by snv_lref, ldrop_inv_gen/
   ]
-| #a #I #G #K #V #T #_ #_ #IHV #IHT #L #d #e #HLK #X #H
+| #a #I #G #K #V #T #_ #_ #IHV #IHT #L #s #d #e #HLK #X #H
   elim (lift_inv_bind1 … H) -H #W #U #HVW #HTU #H destruct
-  /4 width=4/
-| #a #G #K #V #V0 #V1 #T #T1 #l #_ #_ #Hl #HV0 #HV01 #HT1 #IHV #IHT #L #d #e #HLK #X #H
+  /4 width=5 by snv_bind, ldrop_skip/
+| #a #G #K #V #V0 #V1 #T #T1 #l #_ #_ #Hl #HV0 #HV01 #HT1 #IHV #IHT #L #s #d #e #HLK #X #H
   elim (lift_inv_flat1 … H) -H #W #U #HVW #HTU #H destruct
   elim (lift_total V0 d e) #W0 #HVW0
   elim (lift_total V1 d e) #W1 #HVW1
   elim (lift_total T1 (d+1) e) #U1 #HTU1
   @(snv_appl … a … W0 … W1 … U1 l)
-  [1,2: /2 width=4/ | /2 width=7/ |4,5: /2 width=9/ ]
-  @(cpds_lift … HT1 … HLK … HTU) /2 width=1/
-| #G #K #V0 #T #V #l #_ #_ #Hl #HTV #HV0 #IHV0 #IHT #L #d #e #HLK #X #H
+  [1,2,3,4,5: /2 width=10 by cprs_lift, ssta_lift, da_lift/ ]
+  @(cpds_lift … HT1 … HLK … HTU) /2 width=1 by lift_bind/ (**) (* full auto raises typecjhecker failure *)
+| #G #K #V0 #T #V #l #_ #_ #Hl #HTV #HV0 #IHV0 #IHT #L #s #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
-  @(snv_cast … W l) [1,2: /2 width=4/ | /2 width=7/ |4,5: /2 width=9/ ]
+  elim (lift_total V d e)
+  /3 width=12 by snv_cast, cpcs_lift, ssta_lift, da_lift/
 ]
 qed.
 
-lemma snv_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ U ¡[h, g] → ∀K,d,e. ⇩[d, e] L ≡ K →
+lemma snv_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ U ¡[h, g] → ∀K,s,d,e. ⇩[s, d, e] L ≡ K →
                     ∀T. ⇧[d, e] T ≡ U → ⦃G, K⦄ ⊢ T ¡[h, g].
 #h #g #G #L #U #H elim H -G -L -U
-[ #G #L #k #K #d #e #_ #X #H
+[ #G #L #k #K #s #d #e #_ #X #H
   >(lift_inv_sort2 … H) -X -L -d -e //
-| #I #G #L #L0 #W #i #HL0 #_ #IHW #K #d #e #HLK #X #H
+| #I #G #L #L0 #W #i #HL0 #_ #IHW #K #s #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
-    /3 width=8/
-  | lapply (ldrop_conf_ge … HLK … HL0 ?) -L // -Hid /3 width=8/
+  [ elim (ldrop_conf_le … HLK … HL0) -L /2 width=2 by lt_to_le/ #X #HK0 #H
+    elim (ldrop_inv_skip1 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid #K0 #V #HLK0 #HVW #H destruct
+    /3 width=12 by snv_lref/
+  | lapply (ldrop_conf_ge … HLK … HL0 ?) -L /3 width=9 by snv_lref/
   ]
-| #a #I #G #L #W #U #_ #_ #IHW #IHU #K #d #e #HLK #X #H
-  elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct /4 width=4/
-| #a #G #L #W #W0 #W1 #U #U1 #l #_ #_ #Hl #HW0 #HW01 #HU1 #IHW #IHU #K #d #e #HLK #X #H
+| #a #I #G #L #W #U #_ #_ #IHW #IHU #K #s #d #e #HLK #X #H
+  elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct
+  /4 width=5 by snv_bind, ldrop_skip/
+| #a #G #L #W #W0 #W1 #U #U1 #l #_ #_ #Hl #HW0 #HW01 #HU1 #IHW #IHU #K #s #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #V #T #HVW #HTU #H destruct
   lapply (da_inv_lift … Hl … HLK … HVW) -Hl #Hl
   elim (ssta_inv_lift1 … HW0 … HLK … HVW) -HW0 #V0 #HVW0 #HV0
   elim (cprs_inv_lift1 … HW01 … HLK … HVW0) -W0 #V1 #HVW1 #HV01
   elim (cpds_inv_lift1 … HU1 … HLK … HTU) -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/
-| #G #L #W0 #U #W #l #_ #_ #Hl #HUW #HW0 #IHW0 #IHU #K #d #e #HLK #X #H
+  lapply (lift_inj … HY … HVW1) -HY #H destruct
+  /3 width=8 by snv_appl/
+| #G #L #W0 #U #W #l #_ #_ #Hl #HUW #HW0 #IHW0 #IHU #K #s #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #V0 #T #HVW0 #HTU #H destruct
   lapply (da_inv_lift … Hl … HLK … HTU) -Hl #Hl
   elim (ssta_inv_lift1 … HUW … HLK … HTU) -HUW #V #HVW #HTV
-  lapply (cpcs_inv_lift G … HLK … HVW … HVW0 ?) // -W /3 width=4/
+  lapply (cpcs_inv_lift G … HLK … HVW … HVW0 ?) // -W
+  /3 width=8 by snv_cast/
 ]
 qed-.
 
@@ -89,7 +93,7 @@ lemma snv_fqu_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2
   elim (snv_inv_lref … H) -H #I2 #L2 #V2 #H #HV2
   lapply (ldrop_inv_O2 … H) -H #H destruct //
 |2: *
-|5,6: /3 width=7 by snv_inv_lift/
+|5,6: /3 width=8 by snv_inv_lift/
 ]
 [1,3: #a #I #G1 #L1 #V1 #T1 #H elim (snv_inv_bind … H) -H //
 |2,4: * #G1 #L1 #V1 #T1 #H