milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
index 6ae05e9447d760e147f7f8803d22553770138115..fb21e76c94fdeca706e5d3e2768ab6369b5a8fa3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
@@ -13,92 +13,93 @@
 (**************************************************************************)
 
 include "ground/xoa/ex_4_3.ma".
-include "basic_2/notation/relations/topredtysnstrong_4.ma".
+include "basic_2/notation/relations/topredtysnstrong_3.ma".
 include "basic_2/rt_computation/rsx.ma".
 
-(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR EXTENDED RT-TRANSITION *********)
 
 (* Note: this should be an instance of a more general sex *)
 (* Basic_2A1: uses: lcosx *)
-inductive jsx (h) (G): relation lenv ≝
-| jsx_atom: jsx h G (⋆) (⋆)
-| jsx_bind: ∀I,K1,K2. jsx h G K1 K2 →
-            jsx h G (K1.ⓘ[I]) (K2.ⓘ[I])
-| jsx_pair: ∀I,K1,K2,V. jsx h G K1 K2 →
-            G ⊢ ⬈*𝐒[h,V] K2 → jsx h G (K1.ⓑ[I]V) (K2.ⓧ)
+inductive jsx (G): relation lenv ≝
+| jsx_atom: jsx G (⋆) (⋆)
+| jsx_bind: ∀I,K1,K2. jsx G K1 K2 →
+            jsx G (K1.ⓘ[I]) (K2.ⓘ[I])
+| jsx_pair: ∀I,K1,K2,V. jsx G K1 K2 →
+            G ⊢ ⬈*𝐒[V] K2 → jsx G (K1.ⓑ[I]V) (K2.ⓧ)
 .
 
 interpretation
-  "strong normalization for unbound parallel rt-transition (compatibility)"
-  'ToPRedTySNStrong h G L1 L2 = (jsx h G L1 L2).
+  "strong normalization for extended parallel rt-transition (compatibility)"
+  'ToPRedTySNStrong G L1 L2 = (jsx G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact jsx_inv_atom_sn_aux (h) (G):
-     ∀L1,L2. G ⊢ L1 ⊒[h] L2 → L1 = ⋆ → L2 = ⋆.
-#h #G #L1 #L2 * -L1 -L2
+fact jsx_inv_atom_sn_aux (G):
+     ∀L1,L2. G ⊢ L1 ⊒ L2 → L1 = ⋆ → L2 = ⋆.
+#G #L1 #L2 * -L1 -L2
 [ //
 | #I #K1 #K2 #_ #H destruct
 | #I #K1 #K2 #V #_ #_ #H destruct
 ]
 qed-.
 
-lemma jsx_inv_atom_sn (h) (G):
-      ∀L2. G ⊢ ⋆ ⊒[h] L2 → L2 = ⋆.
+lemma jsx_inv_atom_sn (G):
+      ∀L2. G ⊢ ⋆ ⊒ L2 → L2 = ⋆.
 /2 width=5 by jsx_inv_atom_sn_aux/ qed-.
 
-fact jsx_inv_bind_sn_aux (h) (G):
-     ∀L1,L2. G ⊢ L1 ⊒[h] L2 →
+fact jsx_inv_bind_sn_aux (G):
+     ∀L1,L2. G ⊢ L1 ⊒ L2 →
      ∀I,K1. L1 = K1.ⓘ[I] →
-     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
-      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & I = BPair J V & L2 = K2.ⓧ.
-#h #G #L1 #L2 * -L1 -L2
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒ K2 & L2 = K2.ⓘ[I]
+      | ∃∃J,K2,V. G ⊢ K1 ⊒ K2 & G ⊢ ⬈*𝐒[V] K2 & I = BPair J V & L2 = K2.ⓧ.
+#G #L1 #L2 * -L1 -L2
 [ #J #L1 #H destruct
 | #I #K1 #K2 #HK12 #J #L1 #H destruct /3 width=3 by ex2_intro, or_introl/
 | #I #K1 #K2 #V #HK12 #HV #J #L1 #H destruct /3 width=7 by ex4_3_intro, or_intror/
 ]
 qed-.
 
-lemma jsx_inv_bind_sn (h) (G):
-     ∀I,K1,L2. G ⊢ K1.ⓘ[I] ⊒[h] L2 →
-     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
-      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & I = BPair J V & L2 = K2.ⓧ.
+lemma jsx_inv_bind_sn (G):
+      ∀I,K1,L2. G ⊢ K1.ⓘ[I] ⊒ L2 →
+      ∨∨ ∃∃K2. G ⊢ K1 ⊒ K2 & L2 = K2.ⓘ[I]
+       | ∃∃J,K2,V. G ⊢ K1 ⊒ K2 & G ⊢ ⬈*𝐒[V] K2 & I = BPair J V & L2 = K2.ⓧ.
 /2 width=3 by jsx_inv_bind_sn_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: uses: lcosx_inv_pair *)
-lemma jsx_inv_pair_sn (h) (G):
-      ∀I,K1,L2,V. G ⊢ K1.ⓑ[I]V ⊒[h] L2 →
-      ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓑ[I]V
-       | ∃∃K2. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*𝐒[h,V] K2 & L2 = K2.ⓧ.
-#h #G #I #K1 #L2 #V #H elim (jsx_inv_bind_sn … H) -H *
+lemma jsx_inv_pair_sn (G):
+      ∀I,K1,L2,V. G ⊢ K1.ⓑ[I]V ⊒ L2 →
+      ∨∨ ∃∃K2. G ⊢ K1 ⊒ K2 & L2 = K2.ⓑ[I]V
+       | ∃∃K2. G ⊢ K1 ⊒ K2 & G ⊢ ⬈*𝐒[V] K2 & L2 = K2.ⓧ.
+#G #I #K1 #L2 #V #H elim (jsx_inv_bind_sn … H) -H *
 [ /3 width=3 by ex2_intro, or_introl/
 | #J #K2 #X #HK12 #HX #H1 #H2 destruct /3 width=4 by ex3_intro, or_intror/
 ]
 qed-.
 
-lemma jsx_inv_void_sn (h) (G):
-      ∀K1,L2. G ⊢ K1.ⓧ ⊒[h] L2 →
-      ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓧ.
-#h #G #K1 #L2 #H elim (jsx_inv_bind_sn … H) -H *
+lemma jsx_inv_void_sn (G):
+      ∀K1,L2. G ⊢ K1.ⓧ ⊒ L2 →
+      ∃∃K2. G ⊢ K1 ⊒ K2 & L2 = K2.ⓧ.
+#G #K1 #L2 #H elim (jsx_inv_bind_sn … H) -H *
 /2 width=3 by ex2_intro/
 qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma jsx_fwd_bind_sn (h) (G):
-      ∀I1,K1,L2. G ⊢ K1.ⓘ[I1] ⊒[h] L2 →
-      ∃∃I2,K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I2].
-#h #G #I1 #K1 #L2 #H elim (jsx_inv_bind_sn … H) -H *
+lemma jsx_fwd_bind_sn (G):
+      ∀I1,K1,L2. G ⊢ K1.ⓘ[I1] ⊒ L2 →
+      ∃∃I2,K2. G ⊢ K1 ⊒ K2 & L2 = K2.ⓘ[I2].
+#G #I1 #K1 #L2 #H elim (jsx_inv_bind_sn … H) -H *
 /2 width=4 by ex2_2_intro/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: lcosx_O *)
-lemma jsx_refl (h) (G): reflexive … (jsx h G).
-#h #G #L elim L -L /2 width=1 by jsx_atom, jsx_bind/
+lemma jsx_refl (G):
+      reflexive … (jsx G).
+#G #L elim L -L /2 width=1 by jsx_atom, jsx_bind/
 qed.
 
 (* Basic_2A1: removed theorems 2: