update in basic_2 and ground_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_lfpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lfpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lfpx.ma
index 47d066ab6a8409109a9ba9237e0e4219cfa64fd2..44fc48fae862e8f787ed34ee71c31877b231f00c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lfpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lfpx.ma
@@ -13,12 +13,11 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/cpxs_lfpx.ma".
-include "basic_2/rt_computation/csx_drops.ma".
 include "basic_2/rt_computation/csx_cpxs.ma".
 
 (* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
 
-(* Advanced properties ******************************************************)
+(* Properties with uncounted parallel rt-transition on referred entries *****)
 
 (* Basic_2A1: was just: csx_lpx_conf *)
 lemma csx_lfpx_conf: ∀h,o,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →
@@ -27,6 +26,8 @@ lemma csx_lfpx_conf: ∀h,o,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →
 /5 width=3 by csx_intro, lfpx_cpx_trans, lfpx_cpxs_conf/
 qed-.
 
+(* Advanced properties ******************************************************)
+
 lemma csx_abst: ∀h,o,p,G,L,W. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃W⦄ →
                 ∀T. ⦃G, L.ⓛW⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓛ{p}W.T⦄.
 #h #o #p #G #L #W #HW @(csx_ind … HW) -W
@@ -37,7 +38,7 @@ elim (cpx_inv_abst1 … H1) -H1
 elim (tdneq_inv_pair … H2) -H2
 [ #H elim H -H //
 | -IHT #H lapply (csx_cpx_trans … o … HLT0) // -HT
-  #HT0 lapply (csx_lfpx_conf … HT0 … (L.ⓛW0)) -HT0 /4 width=1 by lfpx_pair/
+  #HT0 lapply (csx_lfpx_conf … HT0 … (L.ⓛW0)) -HT0 /4 width=1 by lfpx_pair_refl/
 | -IHW -HT /4 width=3 by csx_cpx_trans, cpx_pair_sn/
 ]
 qed.
@@ -51,7 +52,7 @@ elim (cpx_inv_abbr1 … H1) -H1 *
 [ #V1 #T1 #HLV1 #HLT1 #H destruct
   elim (tdneq_inv_pair … H2) -H2
   [ #H elim H -H //
-  | /4 width=3 by csx_cpx_trans, csx_lfpx_conf, lfpx_pair/
+  | /4 width=3 by csx_cpx_trans, csx_lfpx_conf, lfpx_pair_refl/
   | -IHV /4 width=3 by csx_cpx_trans, cpx_cpxs, cpx_pair_sn/
   ]
 | -IHV -IHT -H2
@@ -59,7 +60,7 @@ elim (cpx_inv_abbr1 … H1) -H1 *
 ]
 qed.
 
-fact csx_appl_theta_aux: â\88\80h,o,p,G,L,U. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Uâ¦\84 â\86\92 â\88\80V1,V2. â¬\86*[1] V1 â\89¡ V2 →
+fact csx_appl_theta_aux: â\88\80h,o,p,G,L,U. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Uâ¦\84 â\86\92 â\88\80V1,V2. â¬\86*[1] V1 â\89\98 V2 →
                          ∀V,T. U = ⓓ{p}V.ⓐV2.T → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
 #h #o #p #G #L #X #H @(csx_ind_cpxs … H) -X
 #X #HVT #IHVT #V1 #V2 #HV12 #V #T #H destruct
@@ -69,34 +70,30 @@ lapply (csx_fwd_bind_dx … HVT) -HVT #HVT
 elim (cpx_inv_appl1 … HL) -HL *
 [ -HV #V0 #Y #HLV10 #HL #H0 destruct
   elim (cpx_inv_abbr1 … HL) -HL *
-  [ #V3 #T3 #HV3 #HLT3 #H0 destruct
-    elim (lift_total V0 0 1) #V4 #HV04
-    elim (eq_term_dec (ⓓ{a}V.ⓐV2.T) (ⓓ{a}V3.ⓐV4.T3))
-    [ -IHVT #H0 destruct
-      elim (eq_false_inv_tpair_sn … H) -H
-      [ -HLV10 -HV3 -HLT3 -HVT
-        >(lift_inj … HV12 … HV04) -V4
-        #H elim H //
-      | * #_ #H elim H //
-      ]
-    | -H -HVT #H
-      lapply (cpx_lift … HLV10 (L.ⓓV) (Ⓕ) … HV12 … HV04) -HLV10 -HV12 /2 width=1 by drop_drop/ #HV24
-      @(IHVT … H … HV04) -IHVT /4 width=1 by cpx_cpxs, cpx_bind, cpx_flat/
+  [ -HVT #V3 #T3 #HV3 #HLT3 #H0 destruct
+    elim (cpx_lifts_sn … HLV10 (Ⓣ) … (L.ⓓV) … HV12) -HLV10 /3 width=1 by drops_refl, drops_drop/ #V4 #HV04 #HV24
+    elim (tdeq_dec h o (ⓓ{p}V.ⓐV2.T) (ⓓ{p}V3.ⓐV4.T3)) #H0
+    [ -IHVT -HV3 -HV24 -HLT3
+      elim (tdeq_inv_pair … H0) -H0 #_ #HV3 #H0
+      elim (tdeq_inv_pair … H0) -H0 #_ #HV24 #HT3
+      elim (tdneq_inv_pair … H) -H #H elim H -H -G -L
+      /3 width=6 by tdeq_inv_lifts_bi, tdeq_pair/
+    | -V1 @(IHVT … H0 … HV04) -o -V0 /4 width=1 by cpx_cpxs, cpx_flat, cpx_bind/
     ]
   | -H -IHVT #T0 #HLT0 #HT0 #H0 destruct
     lapply (csx_cpx_trans … HVT (ⓐV2.T0) ?) /2 width=1 by cpx_flat/ -T #HVT0
-    lapply (csx_inv_lift … L … (Ⓕ) … 1 HVT0 ? ? ?) -HVT0
-    /3 width=5 by csx_cpx_trans, cpx_pair_sn, drop_drop, lift_flat/
+    lapply (csx_inv_lifts … HVT0 (Ⓣ) … L ???) -HVT0
+    /3 width=5 by csx_cpx_trans, cpx_pair_sn, drops_refl, drops_drop, lifts_flat/
   ]
 | -HV -HV12 -HVT -IHVT -H #b #V0 #W0 #W1 #T0 #T1 #_ #_ #_ #H destruct
 | -IHVT -H #b #V0 #V3 #W0 #W1 #T0 #T1 #HLV10 #HV03 #HLW01 #HLT01 #H1 #H2 destruct
-  lapply (cpx_lift … HLV10 (L. ⓓW0) … HV12 … HV03) -HLV10 -HV12 -HV03 /2 width=2 by drop_drop/ #HLV23
+  lapply (cpx_lifts_bi … HLV10 (Ⓣ) … (L.ⓓW0) … HV12 … HV03) -HLV10 -HV12 -HV03 /3 width=1 by drops_refl, drops_drop/ #HLV23
   @csx_abbr /2 width=3 by csx_cpx_trans/ -HV
-  @(csx_lpx_conf … (L.ⓓW0)) /2 width=1 by lpx_pair/ -W1
+  @(csx_lfpx_conf … (L.ⓓW0)) /2 width=1 by lfpx_pair_refl/ -W1
   /4 width=5 by csx_cpxs_trans, cpx_cpxs, cpx_flat/
 ]
 qed-.
 
-lemma csx_appl_theta: ∀h,o,a,V1,V2. ⬆[0, 1] V1 ≡ V2 →
-                      ∀G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] ⓓ{a}V.ⓐV2.T → ⦃G, L⦄ ⊢ ⬈*[h, o] ⓐV1.ⓓ{a}V.T.
+lemma csx_appl_theta: ∀h,o,p,G,L,V,V2,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓓ{p}V.ⓐV2.T⦄ →
+                      ∀V1. ⬆*[1] V1 ≘ V2 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
 /2 width=5 by csx_appl_theta_aux/ qed.