milestone in basic_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 4c8371a0b74f9b8c748e9e9a35140b56ed215879..384d014cbd62fb89841f924c98de9b83b4f05acd 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 +12,83 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predtystrong_5.ma".
+include "basic_2/notation/relations/predtystrong_4.ma".
 include "static_2/syntax/tdeq.ma".
 include "basic_2/rt_transition/cpx.ma".
 
 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
 
-definition csx: ∀h. sd h → relation3 genv lenv term ≝
-                λh,o,G,L. SN … (cpx h G L) (tdeq h o …).
+definition csx: ∀h. relation3 genv lenv term ≝
+                λh,G,L. SN … (cpx h G L) tdeq.
 
 interpretation
    "strong normalization for unbound context-sensitive parallel rt-transition (term)"
-   'PRedTyStrong h o G L T = (csx h o G L T).
+   'PRedTyStrong h G L T = (csx h G L T).
 
 (* Basic eliminators ********************************************************)
 
-lemma csx_ind: ∀h,o,G,L. ∀Q:predicate term.
-               (∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                     (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) →
+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, o] 𝐒⦃T⦄ →  Q T.
-#h #o #G #L #Q #H0 #T1 #H elim H -T1
+               ∀T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q T.
+#h #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,o,G,L,T1.
-                 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄) →
-                 ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄.
+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⦄.
 /4 width=1 by SN_intro/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-fact csx_fwd_pair_sn_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ②{I}V.T → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
-#h #o #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+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
 @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/
 qed-.
 
 (* Basic_1: was just: sn3_gen_head *)
-lemma csx_fwd_pair_sn: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃②{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄.
+lemma csx_fwd_pair_sn: ∀h,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃②{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄.
 /2 width=5 by csx_fwd_pair_sn_aux/ qed-.
 
-fact csx_fwd_bind_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
-                          ∀p,I,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
-#h #o #G #L #U #H elim H -H #U0 #_ #IH #p #I #V #T #H destruct
+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
 @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/
 qed-.
 
 (* Basic_1: was just: sn3_gen_bind *)
-lemma csx_fwd_bind_dx: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+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⦄.
 /2 width=4 by csx_fwd_bind_dx_aux/ qed-.
 
-fact csx_fwd_flat_dx_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
-                          ∀I,V,T. U = ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
-#h #o #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+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
 @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/
 qed-.
 
 (* Basic_1: was just: sn3_gen_flat *)
-lemma csx_fwd_flat_dx: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_flat_dx: ∀h,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 /2 width=5 by csx_fwd_flat_dx_aux/ qed-.
 
-lemma csx_fwd_bind: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ ∧ ⦃G, L.ⓑ{I}V⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+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⦄.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_bind_dx, conj/ qed-.
 
-lemma csx_fwd_flat: ∀h,o,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓕ{I}V.T⦄ →
-                    ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ ∧ ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+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⦄.
 /3 width=3 by csx_fwd_pair_sn, csx_fwd_flat_dx, conj/ qed-.
 
 (* Basic_1: removed theorems 14: