milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
index 31f2e017a2ace0bb5c3cf792a1805440203f8b68..13db8d1f3a1c9f74e48deedad6e9d6f73ea2091f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
@@ -12,91 +12,91 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtystrong_4.ma".
+include "basic_2/notation/relations/predtystrong_3.ma".
 include "static_2/syntax/teqx.ma".
 include "basic_2/rt_transition/cpx.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
-definition csx (h) (G) (L): predicate term ≝
-           SN … (cpx h G L) teqx.
+definition csx (G) (L): predicate term ≝
+           SN … (cpx G L) teqx.
 
 interpretation
-  "strong normalization for unbound context-sensitive parallel rt-transition (term)"
-  'PRedTyStrong h G L T = (csx h G L T).
+  "strong normalization for extended context-sensitive parallel rt-transition (term)"
+  'PRedTyStrong G L T = (csx G L T).
 
 (* Basic eliminators ********************************************************)
 
-lemma csx_ind (h) (G) (L) (Q:predicate …):
-      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒[h] T1 →
-        (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) →
+lemma csx_ind (G) (L) (Q:predicate …):
+      (∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → Q T2) →
         Q T1
       ) →
-      ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T →  Q T.
-#h #G #L #Q #H0 #T1 #H elim H -T1
+      ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T →  Q T.
+#G #L #Q #H0 #T1 #H elim H -T1
 /5 width=1 by SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was just: sn3_pr2_intro *)
-lemma csx_intro (h) (G) (L):
-      ∀T1. (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒[h] T2) →
-      ❪G,L❫ ⊢ ⬈*𝐒[h] T1.
+lemma csx_intro (G) (L):
+      ∀T1. (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒 T2) →
+      ❪G,L❫ ⊢ ⬈*𝐒 T1.
 /4 width=1 by SN_intro/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-fact csx_fwd_pair_sn_aux (h) (G) (L):
-     ∀U. ❪G,L❫ ⊢ ⬈*𝐒[h] U →
-     ∀I,V,T. U = ②[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒[h] V.
-#h #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+fact csx_fwd_pair_sn_aux (G) (L):
+     ∀U. ❪G,L❫ ⊢ ⬈*𝐒 U →
+     ∀I,V,T. U = ②[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒 V.
+#G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #V2 #HLV2 #HV2
-@(IH (②[I]V2.T)) -IH /2 width=3 by cpx_pair_sn/ -HLV2
-#H elim (teqx_inv_pair … H) -H /2 width=1 by/
+@(IH (②[I]V2.T)) -IH /2 width=3 by cpx_pair_sn/ -HLV2 #H
+elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_head *)
-lemma csx_fwd_pair_sn (h) (G) (L):
-      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ②[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒[h] V.
+lemma csx_fwd_pair_sn (G) (L):
+      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒 ②[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒 V.
 /2 width=5 by csx_fwd_pair_sn_aux/ qed-.
 
-fact csx_fwd_bind_dx_aux (h) (G) (L):
-     ∀U. ❪G,L❫ ⊢ ⬈*𝐒[h] U →
-     ∀p,I,V,T. U = ⓑ[p,I]V.T → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒[h] T.
-#h #G #L #U #H elim H -H #U0 #_ #IH #p #I #V #T #H destruct
+fact csx_fwd_bind_dx_aux (G) (L):
+     ∀U. ❪G,L❫ ⊢ ⬈*𝐒 U →
+     ∀p,I,V,T. U = ⓑ[p,I]V.T → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒 T.
+#G #L #U #H elim H -H #U0 #_ #IH #p #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
-@(IH (ⓑ[p, I]V.T2)) -IH /2 width=3 by cpx_bind/ -HLT2
-#H elim (teqx_inv_pair … H) -H /2 width=1 by/
+@(IH (ⓑ[p, I]V.T2)) -IH /2 width=3 by cpx_bind/ -HLT2 #H
+elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_bind *)
-lemma csx_fwd_bind_dx (h) (G) (L):
-      ∀p,I,V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓑ[p,I]V.T → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒[h] T.
+lemma csx_fwd_bind_dx (G) (L):
+      ∀p,I,V,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓑ[p,I]V.T → ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒 T.
 /2 width=4 by csx_fwd_bind_dx_aux/ qed-.
 
-fact csx_fwd_flat_dx_aux (h) (G) (L):
-     ∀U. ❪G,L❫ ⊢ ⬈*𝐒[h] U →
-     ∀I,V,T. U = ⓕ[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒[h] T.
-#h #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+fact csx_fwd_flat_dx_aux (G) (L):
+     ∀U. ❪G,L❫ ⊢ ⬈*𝐒 U →
+     ∀I,V,T. U = ⓕ[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒 T.
+#G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
-@(IH (ⓕ[I]V.T2)) -IH /2 width=3 by cpx_flat/ -HLT2
-#H elim (teqx_inv_pair … H) -H /2 width=1 by/
+@(IH (ⓕ[I]V.T2)) -IH /2 width=3 by cpx_flat/ -HLT2 #H
+elim (teqx_inv_pair … H) -H /2 width=1 by/
 qed-.
 
 (* Basic_1: was just: sn3_gen_flat *)
-lemma csx_fwd_flat_dx (h) (G) (L):
-      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓕ[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒[h] T.
+lemma csx_fwd_flat_dx (G) (L):
+      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓕ[I]V.T → ❪G,L❫ ⊢ ⬈*𝐒 T.
 /2 width=5 by csx_fwd_flat_dx_aux/ qed-.
 
-lemma csx_fwd_bind (h) (G) (L):
-      ∀p,I,V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓑ[p,I]V.T →
-      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒[h] V & ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒[h] T.
+lemma csx_fwd_bind (G) (L):
+      ∀p,I,V,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓑ[p,I]V.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒 V & ❪G,L.ⓑ[I]V❫ ⊢ ⬈*𝐒 T.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_bind_dx, conj/ qed-.
 
-lemma csx_fwd_flat (h) (G) (L):
-      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒[h] ⓕ[I]V.T →
-      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒[h] V & ❪G,L❫ ⊢ ⬈*𝐒[h] T.
+lemma csx_fwd_flat (G) (L):
+      ∀I,V,T. ❪G,L❫ ⊢ ⬈*𝐒 ⓕ[I]V.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒 V & ❪G,L❫ ⊢ ⬈*𝐒 T.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_1: removed theorems 14: