update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / deq_cpr.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/deq_cpr.ma b/matita/matita/contribs/lambdadelta/apps_2/models/deq_cpr.ma
index 74124719e6eb355d28045ccacd8fda08fde6af55..7d648b07543e03d5d9af14c2c6b63a0dbc85cdad 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/deq_cpr.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/deq_cpr.ma
@@ -21,54 +21,62 @@ include "apps_2/models/deq.ma".
 (* Forward lemmas with context-sensitive parallel reduction for terms *******)
 
 lemma cpr_fwd_deq (h) (M): is_model M → is_extensional M →
-                           â\88\80G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\86\92 â¦\83G, Lâ¦\84 ⊢ T1 ≗{M} T2.
+                           â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ≗{M} T2.
 #h #M #H1M #H2M #G #L #T1 #T2 #H @(cpr_ind … H) -G -L -T1 -T2
 [ /2 width=2 by deq_refl/
 | #G #K #V1 #V2 #W2 #_ #IH #HVW2 #gv #v #H
-  elim (li_inv_abbr … H) -H #lv #d #HK #Hd #H
-  @(mr … H1M) [4,5: @(ti_ext_l … H1M … H) |1,2: skip ] -v
-  lapply (lifts_SO_fwd_vlift … gv H1M H2M … HVW2 lv d) -HVW2 #HVW2
-  @(seq_trans … H1M … HVW2) -W2
-  @(seq_trans … H1M) [3: @IH // | skip ] -G -K -V2
-  @(seq_canc_dx … H1M … Hd) -V1 /2 width=1 by ti_lref_vlift_eq/
+  elim (li_inv_abbr … H) -H // #lv #HK #H
+  @(mq … H1M) [4,5: @(ti_comp … H) /2 width=2 by veq_refl/ |1,2: skip ] -v
+  @(mq … H1M)
+  [4: /3 width=1 by seq_sym, ml/ | skip
+  |5: /2 width=2 by lifts_SO_fwd_vpush/ | skip ] -W2
+  >vpush_eq /2 width=1 by/
 | #I #G #K #T #U #i #_ #IH #HTU #gv #v #H
-  elim (li_fwd_bind … H) -H #lv #d #HK #H
-  @(mr … H1M) [4,5: @(ti_ext_l … H1M … H) |1,2: skip ] -v
-  lapply (lifts_SO_fwd_vlift … gv H1M H2M … HTU lv d) -HTU #HTU
-  @(seq_trans … H1M … HTU) -U
-  @(seq_trans … H1M) [3: @IH // | skip ] -G -K -T
-  /2 width=1 by ti_lref_vlift_gt/
+  elim (li_fwd_bind … H) // -H #lv #d #HK #H
+  @(mq … H1M) [4,5: @(ti_comp … H) /2 width=2 by veq_refl/ |1,2: skip ] -v
+  @(mq … H1M)
+  [4: /3 width=1 by seq_sym, ml/ | skip
+  |5: /2 width=2 by lifts_SO_fwd_vpush/ | skip ] -U
+  >vpush_gt /3 width=5 by ml, mq, mr/
 | #p * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #gv #lv #Hlv
-  [ @(mr … H1M) [4,5: @(seq_sym … H1M) @(md … H1M) |1,2: skip ] -p
-    @(seq_trans … H1M) [3: @IHT /3 width=1 by li_abbr/ | skip ] -T2
-    /4 width=1 by ti_comp_l, veq_refl, vlift_comp/
-  | @(mx … H2M) /3 width=1 by li_abst/
+  [ @(mq … H1M) [4,5: /3 width=2 by seq_sym, md/ |1,2: skip ]
+    @mc [3:|*: /2 width=1 by/ ] -p
+    @(seq_trans … H1M) [2: @IHT /2 width=1 by li_abbr/ | skip ] -T1
+    /4 width=1 by ti_comp, vpush_comp, (* 2x *) veq_refl/
+  | /4 width=1 by li_abst, mx/
   ]
 | * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #gv #lv #Hlv
-  [ @(mr … H1M) [4,5: @(seq_sym … H1M) @(ma … H1M) |1,2: skip ]
-    /3 width=1 by mc/
-  | @(mr … H1M) [4,5: @(seq_sym … H1M) @(me … H1M) |1,2: skip ]
+  [ @(mq … H1M) [4,5: /3 width=2 by seq_sym, ma/ |1,2: skip ]
+    /3 width=1 by mp/
+  | @(mq … H1M) [4,5: /3 width=2 by seq_sym, me/ |1,2: skip ]
     /2 width=1 by/
   ]
-| #G #L #V #U1 #U2 #T2 #_ #IH #HTU2 #gv #lv #Hlv
-  @(seq_trans … H1M) [2: @(md … H1M) | skip ]
-  @(seq_trans … H1M) [2: @IH /3 width=1 by li_abbr, veq_refl/ | skip ] -G -L -U1
-  /3 width=1 by lifts_SO_fwd_vlift, seq_sym/
+| #G #L #V #U1 #T1 #T2 #HTU1 #_ #IH #gv #lv #Hlv
+  @(mq … H1M)
+  [4: /3 width=2 by seq_sym, md/ | skip
+  |3: @(seq_trans … H1M) [2: @mz // | skip ]
+  ] /3 width=3 by lifts_SO_fwd_vpush, seq_sym/
 | #G #L #V #T1 #T2 #_ #IH #gv #lv #Hlv
   @(seq_trans … H1M) [2: @(me … H1M) | skip ]
   /2 width=1 by/
 | #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV #_ #IHT #gv #lv #Hlv
-  @(mr … H1M) [4,5: @(seq_sym … H1M) [ @(ma … H1M) | @(md … H1M) ] |1,2: skip ]
-  @(seq_trans … H1M) [3: @IHT /2 width=1 by li_abst/ | skip ] -T2
-  @(mr … H1M) [4,5: @(seq_sym … H1M) [ @(mb … H1M) | @(ti_comp_l … H1M) ] |1,2: skip ]
-  [2: @vlift_comp [2: @(me … H1M) |4: @(veq_refl … H1M) |1,3: skip ] | skip ]
-  /4 width=1 by ti_comp_l, veq_refl, vlift_comp/
+  @(mq … H1M) [4,5: /3 width=2 by seq_sym, ma, md/ |1,2: skip ]
+  @(seq_trans … H1M) [3:|*: /2 width=2 by mb/ ]
+  @mc // -p [ /4 width=5 by seq_trans, seq_sym, me/ ]
+  @(seq_trans … H1M) [2: @IHT /2 width=1 by li_abst/ | skip ] -T1
+  @ti_comp /2 width=1 by veq_refl/
+  @vpush_comp /2 width=1 by veq_refl/
+  /4 width=5 by seq_trans, seq_sym, me/
 | #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV #IHW #IHT #HV2 #gv #lv #Hlv
-  @(mr … H1M) [4,5: @(seq_sym … H1M) [ @(ma … H1M) | @(md … H1M) ] |1,2: skip ]
-  @(mr … H1M) [4,5: @(seq_sym … H1M) [ @(mc … H1M) | @(ma … H1M) ] |1,2: skip ]
-  [2: @IHV // |4: @(md … H1M) |1,3: skip ] -p -V1
-  @(mc … H1M) [ /2 width=1 by lifts_SO_fwd_vlift/ ] -V -V2
-  @(seq_trans … H1M) [2: @IHT /3 width=1 by li_abbr, veq_refl/ | skip ] -T1
-  /4 width=1 by ti_comp_l, veq_refl, vlift_comp/
+  @(mq … H1M) [4,5: /3 width=2 by seq_sym, ma, md/ |1,2: skip ]
+  @(mq … H1M)
+  [4: /4 width=2 by seq_sym, md, mp/ |1: skip
+  |5: /4 width=2 by seq_sym, ma, mc/ |2: skip
+  ]
+  @(seq_trans … H1M) [2: @mh // | skip ]
+  @mc [3:|*: /2 width=1 by mr/ ]
+  @mp [3:|*: /2 width=1 by lifts_SO_fwd_vpush/ ]
+  @(seq_trans … H1M) [2: @IHT /2 width=1 by li_abbr/ | skip ] -T1
+  /4 width=1 by ti_comp, vpush_comp, (* 2x *) veq_refl/
 ]
 qed-.