X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fjsx.ma;h=a318423b5b1ab82ccd979a4a90b1cd5a498e7888;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=94a1ec855107b68d289fdf7201b7d12b0f618924;hpb=a454837a256907d2f83d42ced7be847e10361ea9;p=helm.git

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 94a1ec855..a318423b5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
@@ -12,151 +12,92 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/topredtysnstrong_5.ma".
+include "ground_2/xoa/ex_4_3.ma".
+include "basic_2/notation/relations/topredtysnstrong_4.ma".
 include "basic_2/rt_computation/rsx.ma".
 
 (* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
 
 (* Note: this should be an instance of a more general sex *)
 (* Basic_2A1: uses: lcosx *)
-inductive jsx (h) (G): rtmap → relation lenv ≝
-| jsx_atom: ∀f. jsx h G f (⋆) (⋆)
-| jsx_push: ∀f,I,K1,K2. jsx h G f K1 K2 →
-               jsx h G (⫯f) (K1.ⓘ{I}) (K2.ⓘ{I})
-| jsx_unit: ∀f,I,K1,K2. jsx h G f K1 K2 →
-               jsx h G (↑f) (K1.ⓤ{I}) (K2.ⓧ)
-| jsx_pair: ∀f,I,K1,K2,V. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ →
-               jsx h G f K1 K2 → jsx h G (↑f) (K1.ⓑ{I}V) (K2.ⓧ)
+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 ⊢ ⬈*[h,V] 𝐒❪K2❫ → jsx h G (K1.ⓑ[I]V) (K2.ⓧ)
 .
 
 interpretation
   "strong normalization for unbound parallel rt-transition (compatibility)"
-  'ToPRedTySNStrong h f G L1 L2 = (jsx h G f L1 L2).
+  'ToPRedTySNStrong h G L1 L2 = (jsx h G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
 fact jsx_inv_atom_sn_aux (h) (G):
-     ∀g,L1,L2. G ⊢ L1 ⊒[h,g] L2 → L1 = ⋆ → L2 = ⋆.
-#h #G #g #L1 #L2 * -g -L1 -L2 //
-[ #f #I #K1 #K2 #_ #H destruct
-| #f #I #K1 #K2 #_ #H destruct
-| #f #I #K1 #K2 #V #_ #_ #H destruct
+     ∀L1,L2. G ⊢ L1 ⊒[h] L2 → L1 = ⋆ → L2 = ⋆.
+#h #G #L1 #L2 * -L1 -L2
+[ //
+| #I #K1 #K2 #_ #H destruct
+| #I #K1 #K2 #V #_ #_ #H destruct
 ]
 qed-.
 
-lemma jsx_inv_atom_sn (h) (G): ∀g,L2. G ⊢ ⋆ ⊒[h,g] L2 → L2 = ⋆.
-/2 width=7 by jsx_inv_atom_sn_aux/ qed-.
-
-fact jsx_inv_push_sn_aux (h) (G):
-     ∀g,L1,L2. G ⊢ L1 ⊒[h,g] L2 →
-     ∀f,I,K1. g = ⫯f → L1 = K1.ⓘ{I} →
-     ∃∃K2. G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓘ{I}.
-#h #G #g #L1 #L2 * -g -L1 -L2
-[ #f #g #J #L1 #_ #H destruct
-| #f #I #K1 #K2 #HK12 #g #J #L1 #H1 #H2 destruct
-  <(injective_push … H1) -g /2 width=3 by ex2_intro/
-| #f #I #K1 #K2 #_ #g #J #L1 #H
-  elim (discr_next_push … H)
-| #f #I #K1 #K2 #V #_ #_ #g #J #L1 #H
-  elim (discr_next_push … H)
+lemma jsx_inv_atom_sn (h) (G): ∀L2. G ⊢ ⋆ ⊒[h] 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 →
+     ∀I,K1. L1 = K1.ⓘ[I] →
+     ∨∨ ∃∃K2. G ⊢ K1 ⊒[h] K2 & L2 = K2.ⓘ[I]
+      | ∃∃J,K2,V. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*[h,V] 𝐒❪K2❫  & I = BPair J V & L2 = K2.ⓧ.
+#h #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_push_sn (h) (G):
-      ∀f,I,K1,L2. G ⊢ K1.ⓘ{I} ⊒[h,⫯f] L2 →
-      ∃∃K2. G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓘ{I}.
-/2 width=5 by jsx_inv_push_sn_aux/ qed-.
-
-fact jsx_inv_unit_sn_aux (h) (G):
-     ∀g,L1,L2. G ⊢ L1 ⊒[h,g] L2 →
-     ∀f,I,K1. g = ↑f → L1 = K1.ⓤ{I} →
-     ∃∃K2. G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓧ.
-#h #G #g #L1 #L2 * -g -L1 -L2
-[ #f #g #J #L1 #_ #H destruct
-| #f #I #K1 #K2 #_ #g #J #L1 #H
-  elim (discr_push_next … H)
-| #f #I #K1 #K2 #HK12 #g #J #L1 #H1 #H2 destruct
-  <(injective_next … H1) -g /2 width=3 by ex2_intro/
-| #f #I #K1 #K2 #V #_ #_ #g #J #L1 #_ #H destruct
-]
-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 ⊢ ⬈*[h,V] 𝐒❪K2❫  & I = BPair J V & L2 = K2.ⓧ.
+/2 width=3 by jsx_inv_bind_sn_aux/ qed-.
 
-lemma jsx_inv_unit_sn (h) (G):
-      ∀f,I,K1,L2. G ⊢ K1.ⓤ{I} ⊒[h,↑f] L2 →
-      ∃∃K2. G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓧ.
-/2 width=6 by jsx_inv_unit_sn_aux/ qed-.
-
-fact jsx_inv_pair_sn_aux (h) (G):
-     ∀g,L1,L2. G ⊢ L1 ⊒[h,g] L2 →
-     ∀f,I,K1,V. g = ↑f → L1 = K1.ⓑ{I}V →
-     ∃∃K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄  & G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓧ.
-#h #G #g #L1 #L2 * -g -L1 -L2
-[ #f #g #J #L1 #W #_ #H destruct
-| #f #I #K1 #K2 #_ #g #J #L1 #W #H
-  elim (discr_push_next … H)
-| #f #I #K1 #K2 #_ #g #J #L1 #W #_ #H destruct
-| #f #I #K1 #K2 #V #HV #HK12 #g #J #L1 #W #H1 #H2 destruct
-  <(injective_next … H1) -g /2 width=4 by ex3_intro/
-]
-qed-.
+(* Advanced inversion lemmas ************************************************)
 
 (* Basic_2A1: uses: lcosx_inv_pair *)
 lemma jsx_inv_pair_sn (h) (G):
-      ∀f,I,K1,L2,V. G ⊢ K1.ⓑ{I}V ⊒[h,↑f] L2 →
-      ∃∃K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄  & G ⊢ K1 ⊒[h,f] K2 & L2 = K2.ⓧ.
-/2 width=6 by jsx_inv_pair_sn_aux/ qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma jsx_inv_pair_sn_gen (h) (G): ∀g,I,K1,L2,V. G ⊢ K1.ⓑ{I}V ⊒[h,g] L2 →
-      ∨∨ ∃∃f,K2. G ⊢ K1 ⊒[h,f] K2 & g = ⫯f & L2 = K2.ⓑ{I}V
-       | ∃∃f,K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄  & G ⊢ K1 ⊒[h,f] K2 & g = ↑f & L2 = K2.ⓧ.
-#h #G #g #I #K1 #L2 #V #H
-elim (pn_split g) * #f #Hf destruct
-[ elim (jsx_inv_push_sn … H) -H /3 width=5 by ex3_2_intro, or_introl/
-| elim (jsx_inv_pair_sn … H) -H /3 width=6 by ex4_2_intro, or_intror/
+      ∀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 ⊢ ⬈*[h,V] 𝐒❪K2❫ & L2 = K2.ⓧ.
+#h #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 *
+/2 width=3 by ex2_intro/
+qed-.
+
 (* Advanced forward lemmas **************************************************)
 
 lemma jsx_fwd_bind_sn (h) (G):
-      ∀g,I1,K1,L2. G ⊢ K1.ⓘ{I1} ⊒[h,g] L2 →
-      ∃∃I2,K2. G ⊢ K1 ⊒[h,⫱g] K2 & L2 = K2.ⓘ{I2}.
-#h #G #g #I1 #K1 #L2
-elim (pn_split g) * #f #Hf destruct
-[ #H elim (jsx_inv_push_sn … H) -H
-| cases I1 -I1 #I1
-  [ #H elim (jsx_inv_unit_sn … H) -H
-  | #V #H elim (jsx_inv_pair_sn … H) -H
-  ]
-]
+      ∀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 *
 /2 width=4 by ex2_2_intro/
 qed-.
 
-(* Basic properties *********************************************************)
-
-lemma jsx_eq_repl_back (h) (G): ∀L1,L2. eq_repl_back … (λf. G ⊢ L1 ⊒[h,f] L2).
-#h #G #L1 #L2 #f1 #H elim H -L1 -L2 -f1 //
-[ #f #I #L1 #L2 #_ #IH #x #H
-  elim (eq_inv_px … H) -H /3 width=3 by jsx_push/
-| #f #I #L1 #L2 #_ #IH #x #H
-  elim (eq_inv_nx … H) -H /3 width=3 by jsx_unit/
-| #f #I #L1 #L2 #V #HV #_ #IH #x #H
-  elim (eq_inv_nx … H) -H /3 width=3 by jsx_pair/
-]
-qed-.
-
-lemma jsx_eq_repl_fwd (h) (G): ∀L1,L2. eq_repl_fwd … (λf. G ⊢ L1 ⊒[h,f] L2).
-#h #G #L1 #L2 @eq_repl_sym /2 width=3 by jsx_eq_repl_back/
-qed-.
-
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: lcosx_O *)
-lemma jsx_refl (h) (G): ∀f. 𝐈⦃f⦄ → reflexive … (jsx h G f).
-#h #G #f #Hf #L elim L -L
-/3 width=3 by jsx_eq_repl_back, jsx_push, eq_push_inv_isid/
+lemma jsx_refl (h) (G): reflexive … (jsx h G).
+#h #G #L elim L -L /2 width=1 by jsx_atom, jsx_bind/
 qed.
 
 (* Basic_2A1: removed theorems 2: