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 7fe343b8a557d90ada8d869f9266d3d26ccca4ab..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
@@ -12,83 +12,91 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtystrong_4.ma".
-include "static_2/syntax/tdeq.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. relation3 genv lenv term ≝
-                λh,G,L. SN … (cpx h G L) tdeq.
+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 term.
-               (∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-                     (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) →
-                     Q T1
-               ) →
-               ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q T.
-#h #G #L #Q #H0 #T1 #H elim H -T1
+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 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⦄ ⊢ ⬈*[h] 𝐒⦃T2⦄) →
-                 ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ②{I}V.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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 (tdeq_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,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃②{I}V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀p,I,V,T. U = ⓑ{p,I}V.T → ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃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 (tdeq_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,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ → ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃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⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ⓕ{I}V.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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 (tdeq_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,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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,p,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                    ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L.ⓑ{I}V⦄ ⊢ ⬈*[h] 𝐒⦃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,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ →
-                    ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃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:
@@ -98,6 +106,6 @@ lemma csx_fwd_flat: ∀h,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ 
             sn3_appl_appls sn3_bind sn3_appl_bind sn3_appls_bind
 *)
 (* Basic_2A1: removed theorems 6:
-              csxa_ind csxa_intro csxa_cpxs_trans csxa_intro_cpx 
+              csxa_ind csxa_intro csxa_cpxs_trans csxa_intro_cpx
               csx_csxa csxa_csx
 *)