update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
index f0a53e660691063120d6c34f2e8e67a7dc496a60..5bbdcb1801880c446b3f2b315ef151e3c3993aa4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
@@ -22,14 +22,14 @@ include "basic_2/rt_computation/rsx_rsx.ma".
 
 (* Basic_2A1: uses: lsx_intro_alt *)
 lemma rsx_intro_lpxs (h) (G):
-      ∀L1,T. (∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → G ⊢ ⬈*[h,T] 𝐒❪L2❫) →
-      G ⊢ ⬈*[h,T] 𝐒❪L1❫.
+      ∀L1,T. (∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → G ⊢ ⬈*𝐒[h,T] L2) →
+      G ⊢ ⬈*𝐒[h,T] L1.
 /4 width=1 by lpx_lpxs, rsx_intro/ qed-.
 
 (* Basic_2A1: uses: lsx_lpxs_trans *)
 lemma rsx_lpxs_trans (h) (G):
-      ∀L1,T. G ⊢ ⬈*[h,T] 𝐒❪L1❫ →
-      ∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → G ⊢ ⬈*[h,T] 𝐒❪L2❫.
+      ∀L1,T. G ⊢ ⬈*𝐒[h,T] L1 →
+      ∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → G ⊢ ⬈*𝐒[h,T] L2.
 #h #G #L1 #T #HL1 #L2 #H @(lpxs_ind_dx … H) -L2
 /2 width=3 by rsx_lpx_trans/
 qed-.
@@ -37,11 +37,11 @@ qed-.
 (* Eliminators with unbound rt-computation for full local environments ******)
 
 lemma rsx_ind_lpxs_reqx (h) (G) (T) (Q:predicate lenv):
-      (∀L1. G ⊢ ⬈*[h,T] 𝐒❪L1❫ →
-            (∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
-            Q L1
+      (∀L1. G ⊢ ⬈*𝐒[h,T] L1 →
+        (∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
+        Q L1
       ) →
-      ∀L1. G ⊢ ⬈*[h,T] 𝐒❪L1❫  →
+      ∀L1. G ⊢ ⬈*𝐒[h,T] L1 →
       ∀L0. ❪G,L1❫ ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[T] L2 → Q L2.
 #h #G #T #Q #IH #L1 #H @(rsx_ind … H) -L1
 #L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02
@@ -62,11 +62,11 @@ qed-.
 
 (* Basic_2A1: uses: lsx_ind_alt *)
 lemma rsx_ind_lpxs (h) (G) (T) (Q:predicate lenv):
-      (∀L1. G ⊢ ⬈*[h,T] 𝐒❪L1❫ →
-            (∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
-            Q L1
+      (∀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 #IH #L #HL
 @(rsx_ind_lpxs_reqx … IH … HL) -IH -HL // (**) (* full auto fails *)
 qed-.
@@ -74,10 +74,10 @@ qed-.
 (* Advanced properties ******************************************************)
 
 fact rsx_bind_lpxs_aux (h) (G):
-     ∀p,I,L1,V. G ⊢ ⬈*[h,V] 𝐒❪L1❫ →
-     ∀Y,T. G ⊢ ⬈*[h,T] 𝐒❪Y❫ →
+     ∀p,I,L1,V. G ⊢ ⬈*𝐒[h,V] L1 →
+     ∀Y,T. G ⊢ ⬈*𝐒[h,T] Y →
      ∀L2. Y = L2.ⓑ[I]V → ❪G,L1❫ ⊢ ⬈*[h] L2 →
-     G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L2❫.
+     G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L2.
 #h #G #p #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #_ #IHL1 #Y #T #H @(rsx_ind_lpxs … H) -Y
 #Y #HY #IHY #L2 #H #HL12 destruct
@@ -95,16 +95,16 @@ qed-.
 
 (* Basic_2A1: uses: lsx_bind *)
 lemma rsx_bind (h) (G):
-      ∀p,I,L,V. G ⊢ ⬈*[h,V] 𝐒❪L❫ →
-      ∀T. G ⊢ ⬈*[h,T] 𝐒❪L.ⓑ[I]V❫ →
-      G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L❫.
+      ∀p,I,L,V. G ⊢ ⬈*𝐒[h,V] L →
+      ∀T. G ⊢ ⬈*𝐒[h,T] L.ⓑ[I]V →
+      G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L.
 /2 width=3 by rsx_bind_lpxs_aux/ qed.
 
 (* Basic_2A1: uses: lsx_flat_lpxs *)
 lemma rsx_flat_lpxs (h) (G):
-      ∀I,L1,V. G ⊢ ⬈*[h,V] 𝐒❪L1❫ →
-      ∀L2,T. G ⊢ ⬈*[h,T] 𝐒❪L2❫ → ❪G,L1❫ ⊢ ⬈*[h] L2 →
-      G ⊢ ⬈*[h,ⓕ[I]V.T] 𝐒❪L2❫.
+      ∀I,L1,V. G ⊢ ⬈*𝐒[h,V] L1 →
+      ∀L2,T. G ⊢ ⬈*𝐒[h,T] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2 →
+      G ⊢ ⬈*𝐒[h,ⓕ[I]V.T] L2.
 #h #G #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #HL1 #IHL1 #L2 #T #H @(rsx_ind_lpxs … H) -L2
 #L2 #HL2 #IHL2 #HL12 @rsx_intro_lpxs
@@ -121,15 +121,15 @@ qed-.
 
 (* Basic_2A1: uses: lsx_flat *)
 lemma rsx_flat (h) (G):
-      ∀I,L,V. G ⊢ ⬈*[h,V] 𝐒❪L❫ →
-      ∀T. G ⊢ ⬈*[h,T] 𝐒❪L❫ → G ⊢ ⬈*[h,ⓕ[I]V.T] 𝐒❪L❫.
+      ∀I,L,V. G ⊢ ⬈*𝐒[h,V] L →
+      ∀T. G ⊢ ⬈*𝐒[h,T] L → G ⊢ ⬈*𝐒[h,ⓕ[I]V.T] L.
 /2 width=3 by rsx_flat_lpxs/ qed.
 
 fact rsx_bind_lpxs_void_aux (h) (G):
-     ∀p,I,L1,V. G ⊢ ⬈*[h,V] 𝐒❪L1❫ →
-     ∀Y,T. G ⊢ ⬈*[h,T] 𝐒❪Y❫ →
+     ∀p,I,L1,V. G ⊢ ⬈*𝐒[h,V] L1 →
+     ∀Y,T. G ⊢ ⬈*𝐒[h,T] Y →
      ∀L2. Y = L2.ⓧ → ❪G,L1❫ ⊢ ⬈*[h] L2 →
-     G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L2❫.
+     G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L2.
 #h #G #p #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #_ #IHL1 #Y #T #H @(rsx_ind_lpxs … H) -Y
 #Y #HY #IHY #L2 #H #HL12 destruct
@@ -146,7 +146,7 @@ elim (rneqx_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
 qed-.
 
 lemma rsx_bind_void (h) (G):
-      ∀p,I,L,V. G ⊢ ⬈*[h,V] 𝐒❪L❫ →
-      ∀T. G ⊢ ⬈*[h,T] 𝐒❪L.ⓧ❫ →
-      G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L❫.
+      ∀p,I,L,V. G ⊢ ⬈*𝐒[h,V] L →
+      ∀T. G ⊢ ⬈*𝐒[h,T] L.ⓧ →
+      G ⊢ ⬈*𝐒[h,ⓑ[p,I]V.T] L.
 /2 width=3 by rsx_bind_lpxs_void_aux/ qed.