milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_rsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_rsx.ma
index e5e662dc6b57ead0adfd9df6a382dd88d44aa5ad..44d8ac0299c1a52c6f109411111f1e97eb935e6d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_rsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_rsx.ma
@@ -16,45 +16,44 @@ include "basic_2/rt_computation/rsx_drops.ma".
 include "basic_2/rt_computation/rsx_lpxs.ma".
 include "basic_2/rt_computation/jsx.ma".
 
-(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR EXTENDED RT-TRANSITION *********)
 
 (* Properties with strongly normalizing referred local environments *********)
 
 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
-lemma rsx_cpx_trans_jsx (h) (G):
-      ∀L0,T1,T2. ⦃G,L0⦄ ⊢ T1 ⬈[h] T2 →
-      ∀f,L. G ⊢ L0 ⊒[h,f] L →
-      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
-#h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2
+lemma rsx_cpx_trans_jsx (G):
+      ∀L0,T1,T2. ❪G,L0❫ ⊢ T1 ⬈ T2 →
+      ∀L. G ⊢ L0 ⊒ L → G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
+#G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2
 [ //
 | //
-| #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #L #HK0 #HL
-  elim (jsx_inv_pair_sn_gen … HK0) -HK0 *
-  [ #f #K #HK0 #H1 #H2 destruct
+| #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #L #HK0 #HL
+  elim (jsx_inv_pair_sn … HK0) -HK0 *
+  [ #K #HK0 #H destruct
     /4 width=8 by rsx_lifts, rsx_fwd_pair, drops_refl, drops_drop/
-  | #f #K #HV1 #HK0 #H1 #H2 destruct
+  | #K #HK0 #HV1 #H destruct
     /4 width=8 by rsx_lifts, drops_refl, drops_drop/
   ]
-| #I0 #G #K0 #T #U #i #_ #IH #HTU #g #L #HK0 #HL
+| #I0 #G #K0 #T #U #i #_ #IH #HTU #L #HK0 #HL
   elim (jsx_fwd_bind_sn … HK0) -HK0 #I #K #HK0 #H destruct
   /6 width=8 by rsx_inv_lifts, rsx_lifts, drops_refl, drops_drop/
-| #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
+| #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #HL0 #HL
   elim (rsx_inv_bind_void … HL) -HL
   /4 width=2 by jsx_pair, rsx_bind_void/
-| #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
+| #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #HL0 #HL
   elim (rsx_inv_flat … HL) -HL /3 width=2 by rsx_flat/
-| #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #f #L #HL0 #HL
+| #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #L #HL0 #HL
   elim (rsx_inv_bind_void … HL) -HL #HV #HU1
   /5 width=8 by rsx_inv_lifts, drops_refl, drops_drop/
-| #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
+| #G #L0 #V #T1 #T2 #_ #IHT12 #L #HL0 #HL
   elim (rsx_inv_flat … HL) -HL /2 width=2 by/
-| #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
+| #G #L0 #V1 #V2 #T #_ #IHV12 #L #HL0 #HL
   elim (rsx_inv_flat … HL) -HL /2 width=2 by/
-| #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
+| #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #HL0 #HL
   elim (rsx_inv_flat … HL) -HL #HV1 #HL
   elim (rsx_inv_bind_void … HL) -HL #HW1 #HT1
   /4 width=2 by jsx_pair, rsx_bind_void, rsx_flat/
-| #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
+| #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #L #HL0 #HL
   elim (rsx_inv_flat … HL) -HL #HV1 #HL
   elim (rsx_inv_bind_void … HL) -HL #HW1 #HT1
   /6 width=8 by jsx_pair, rsx_lifts, rsx_bind_void, rsx_flat, drops_refl, drops_drop/
@@ -64,15 +63,15 @@ qed-.
 (* Advanced properties of strongly normalizing referred local environments **)
 
 (* Basic_2A1: uses: lsx_cpx_trans_O *)
-lemma rsx_cpx_trans (h) (G):
-      â\88\80L,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 →
-      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
+lemma rsx_cpx_trans (G):
+      â\88\80L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 →
+      G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
 /3 width=6 by rsx_cpx_trans_jsx, jsx_refl/ qed-.
 
-lemma rsx_cpxs_trans (h) (G):
-      â\88\80L,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 →
-      G ⊢ ⬈*[h,T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h,T2] 𝐒⦃L⦄.
-#h #G #L #T1 #T2 #H
-@(cpxs_ind_dx ???????? H) -T1 //
+lemma rsx_cpxs_trans (G):
+      â\88\80L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T2 →
+      G ⊢ ⬈*𝐒[T1] L → G ⊢ ⬈*𝐒[T2] L.
+#G #L #T1 #T2 #H
+@(cpxs_ind_dx ??????? H) -T1 //
 /3 width=3 by rsx_cpx_trans/
 qed-.