update in basic_2

[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..35e326136b35ddf0c997fdd4b22a9fe466264cd4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
@@ -13,27 +13,27 @@
 (**************************************************************************)
 
 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)"
-   'PRedTySNStrong h T G L = (rsx h G T L).
+  "strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
+  'PRedTySNStrong h T G L = (rsx h G T L).
 
 (* Basic eliminators ********************************************************)
 
 (* Basic_2A1: uses: lsx_ind *)
-lemma rsx_ind (h) (G) (T) (Q:predicate lenv):
-      (∀L1. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ →
-            (∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
-            Q L1
+lemma rsx_ind (h) (G) (T) (Q:predicate …):
+      (∀L1. G ⊢ ⬈*𝐒[h,T] L1 →
+        (∀L2. ❪G,L1❫ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
+        Q L1
       ) →
-      ∀L. G ⊢ ⬈*[h,T] 𝐒⦃L⦄ →  Q L.
+      ∀L. G ⊢ ⬈*𝐒[h,T] L →  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 ⊢ ⬈*[h,T] 𝐒⦃L1⦄.
+      (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*ð\9d\90\92[h,T] L2) →
+      G ⊢ ⬈*𝐒[h,T] L1.
 /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 ⊢ ⬈*[h,V] 𝐒⦃L⦄.
+      ∀I,L,V,T. G ⊢ ⬈*𝐒[h,②[I]V.T] L →
+      G ⊢ ⬈*𝐒[h,V] L.
 #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 ⊢ ⬈*[h,T] 𝐒⦃L⦄.
-#h #G #I #L #V #T #H 
+      ∀I,L,V,T. G ⊢ ⬈*𝐒[h,ⓕ[I]V.T] L →
+      G ⊢ ⬈*𝐒[h,T] L.
+#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):
-     ∀L. G ⊢ ⬈*[h,#0] 𝐒⦃L⦄ →
-     ∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+     ∀L. G ⊢ ⬈*𝐒[h,#0] L →
+     ∀I,K,V. L = K.ⓑ[I]V → G ⊢ ⬈*𝐒[h,V] 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):
-      ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒⦃K.ⓑ{I}V⦄ → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+      ∀I,K,V. G ⊢ ⬈*𝐒[h,#0] K.ⓑ[I]V → G ⊢ ⬈*𝐒[h,V] K.
 /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⦄ →
-      ∧∧ G ⊢ ⬈*[h,V] 𝐒⦃L⦄ & G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
+      ∀I,L,V,T. G ⊢ ⬈*𝐒[h,ⓕ[I]V.T] L →
+      ∧∧ G ⊢ ⬈*𝐒[h,V] L & G ⊢ ⬈*𝐒[h,T] L.
 /3 width=3 by rsx_fwd_pair_sn, rsx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_2A1: removed theorems 9: