update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
index 43e4b046135cdf4e7933b071c21df500d536b6fd..81e3d915426ee3bde30c5c46902c2984857aac24 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
@@ -13,13 +13,13 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/predtysnstrong_4.ma".
-include "static_2/static/rdeq.ma".
+include "static_2/static/reqx.ma".
 include "basic_2/rt_transition/lpx.ma".
 
 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
 
 definition rsx (h) (G) (T): predicate lenv ≝
-           SN … (lpx h G) (rdeq T).
+           SN … (lpx h G) (reqx T).
 
 interpretation
    "strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
@@ -29,11 +29,11 @@ interpretation
 
 (* Basic_2A1: uses: lsx_ind *)
 lemma rsx_ind (h) (G) (T) (Q:predicate lenv):
-      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
-            (â\88\80L2. â¦\83G,L1â¦\84 ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
+      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+            (â\88\80L2. â\9dªG,L1â\9d« ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
             Q L1
       ) →
-      â\88\80L. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Lâ¦\84 →  Q L.
+      â\88\80L. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªLâ\9d« →  Q L.
 #h #G #T #Q #H0 #L1 #H elim H -L1
 /5 width=1 by SN_intro/
 qed-.
@@ -43,50 +43,50 @@ qed-.
 (* Basic_2A1: uses: lsx_intro *)
 lemma rsx_intro (h) (G) (T):
       ∀L1.
-      (â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] L2 â\86\92 (L1 â\89\9b[T] L2 â\86\92 â\8a¥) â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84) →
-      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84.
+      (â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] L2 â\86\92 (L1 â\89\9b[T] L2 â\86\92 â\8a¥) â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d«) →
+      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d«.
 /5 width=1 by SN_intro/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
 (* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
 lemma rsx_fwd_pair_sn (h) (G):
-      ∀I,L,V,T. G ⊢ ⬈*[h,②{I}V.T] 𝐒⦃L⦄ →
-      G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Lâ¦\84.
+      ∀I,L,V,T. G ⊢ ⬈*[h,②[I]V.T] 𝐒❪L❫ →
+      G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªLâ\9d«.
 #h #G #I #L #V #T #H
 @(rsx_ind … H) -L #L1 #_ #IHL1
 @rsx_intro #L2 #HL12 #HnL12
-/4 width=3 by rdeq_fwd_pair_sn/
+/4 width=3 by reqx_fwd_pair_sn/
 qed-.
 
 (* Basic_2A1: uses: lsx_fwd_flat_dx *)
 lemma rsx_fwd_flat_dx (h) (G):
-      ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄ →
-      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Lâ¦\84.
-#h #G #I #L #V #T #H 
+      ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ[I]V.T] 𝐒❪L❫ →
+      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªLâ\9d«.
+#h #G #I #L #V #T #H
 @(rsx_ind … H) -L #L1 #_ #IHL1
 @rsx_intro #L2 #HL12 #HnL12
-/4 width=3 by rdeq_fwd_flat_dx/
+/4 width=3 by reqx_fwd_flat_dx/
 qed-.
 
 fact rsx_fwd_pair_aux (h) (G):
-     â\88\80L. G â\8a¢ â¬\88*[h,#0] ð\9d\90\92â¦\83Lâ¦\84 →
-     ∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+     â\88\80L. G â\8a¢ â¬\88*[h,#0] ð\9d\90\92â\9dªLâ\9d« →
+     ∀I,K,V. L = K.ⓑ[I]V → G ⊢ ⬈*[h,V] 𝐒❪K❫.
 #h #G #L #H
 @(rsx_ind … H) -L #L1 #_ #IH #I #K1 #V #H destruct
-/5 width=5 by lpx_pair, rsx_intro, rdeq_fwd_zero_pair/
+/5 width=5 by lpx_pair, rsx_intro, reqx_fwd_zero_pair/
 qed-.
 
 lemma rsx_fwd_pair (h) (G):
-      â\88\80I,K,V. G â\8a¢ â¬\88*[h,#0] ð\9d\90\92â¦\83K.â\93\91{I}Vâ¦\84 â\86\92 G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Kâ¦\84.
+      â\88\80I,K,V. G â\8a¢ â¬\88*[h,#0] ð\9d\90\92â\9dªK.â\93\91[I]Vâ\9d« â\86\92 G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªKâ\9d«.
 /2 width=4 by rsx_fwd_pair_aux/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: lsx_inv_flat *)
 lemma rsx_inv_flat (h) (G):
-      ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄ →
-      â\88§â\88§ G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Lâ¦\84 & G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Lâ¦\84.
+      ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ[I]V.T] 𝐒❪L❫ →
+      â\88§â\88§ G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªLâ\9d« & G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªLâ\9d«.
 /3 width=3 by rsx_fwd_pair_sn, rsx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_2A1: removed theorems 9: