X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fsstas%2Fsstas.etc;h=285cc96913683ae12df0645b20bca22bb71c5cbb;hb=a2092f7ba4c7c566ea90653ff57e4623ab94d8d5;hp=37d8cdb68103d8a917650d40a80f309dd85b7c7c;hpb=18bc3082b332504f60345245e716b62ae628e3a7;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas.etc
index 37d8cdb68..285cc9691 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas.etc
@@ -12,95 +12,69 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/statictypestar_6.ma".
 include "basic_2/static/ssta.ma".
 
-(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
+(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
 
-inductive sstas (h:sh) (g:sd h) (L:lenv): relation term ≝
-| sstas_refl: ∀T,U. ⦃h, L⦄ ⊢ T •[g, 0] U → sstas h g L T T
-| sstas_step: ∀T,U1,U2,l. ⦃h, L⦄ ⊢ T •[g, l+1] U1 → sstas h g L U1 U2 →
-              sstas h g L T U2.
+definition sstas: ∀h. sd h → relation4 genv lenv term term ≝
+                  λh,g,G,L. star … (ssta_step h g G L).
 
-interpretation "stratified unwind (term)"
-   'StaticTypeStar h g L T U = (sstas h g L T U).
+interpretation "iterated stratified static type assignment (term)"
+   'StaticTypeStar h g G L T U = (sstas h g G L T U).
 
 (* Basic eliminators ********************************************************)
 
-fact sstas_ind_alt_aux: ∀h,g,L,U2. ∀R:predicate term.
-                        (∀T. ⦃h, L⦄ ⊢ U2 •[g , 0] T → R U2) →
-                        (∀T,U1,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U1 →
-                                  ⦃h, L⦄ ⊢ U1 •* [g] U2 → R U1 → R T
-                        ) →
-                        ∀T,U. ⦃h, L⦄ ⊢ T •*[g] U → U = U2 → R T.
-#h #g #L #U2 #R #H1 #H2 #T #U #H elim H -H -T -U /2 width=2/ /3 width=5/
+lemma sstas_ind: ∀h,g,G,L,T. ∀R:predicate term.
+                 R T → (
+                    ∀U1,U2,l. ⦃G, L⦄ ⊢ T •* [h, g] U1 →  ⦃G, L⦄ ⊢ U1 •[h, g] ⦃l+1, U2⦄ →
+                    R U1 → R U2
+                 ) →
+                 ∀U. ⦃G, L⦄ ⊢ T •*[h, g] U → R U.
+#h #g #G #L #T #R #IH1 #IH2 #U #H elim H -U //
+#U1 #U2 #H * /2 width=5/
 qed-.
 
-lemma sstas_ind_alt: ∀h,g,L,U2. ∀R:predicate term.
-                     (∀T. ⦃h, L⦄ ⊢ U2 •[g , 0] T → R U2) →
-                     (∀T,U1,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U1 →
-                               ⦃h, L⦄ ⊢ U1 •* [g] U2 → R U1 → R T
-                     ) →
-                     ∀T. ⦃h, L⦄ ⊢ T •*[g] U2 → R T.
-/3 width=9 by sstas_ind_alt_aux/ qed-.
-                         
-(* Basic inversion lemmas ***************************************************)
-
-fact sstas_inv_sort1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U → ∀k. T = ⋆k →
-                          ∀l. deg h g k l → U = ⋆((next h)^l k).
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #U0 #HU0 #k #H #l #Hkl destruct
-  elim (ssta_inv_sort1 … HU0) -L #HkO #_ -U0
-  >(deg_mono … Hkl HkO) -g -l //
-| #T0 #U0 #l0 #HTU0 #_ #IHU0 #k #H #l #Hkl destruct
-  elim (ssta_inv_sort1 … HTU0) -L #HkS #H destruct
-  lapply (deg_mono … Hkl HkS) -Hkl #H destruct
-  >(IHU0 (next h k) ? l0) -IHU0 // /2 width=1/ >iter_SO >iter_n_Sm //
-]
-qed.
+lemma sstas_ind_dx: ∀h,g,G,L,U2. ∀R:predicate term.
+                    R U2 → (
+                       ∀T,U1,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •* [h, g] U2 →
+                       R U1 → R T
+                    ) →
+                    ∀T. ⦃G, L⦄ ⊢ T •*[h, g] U2 → R T.
+#h #g #G #L #U2 #R #IH1 #IH2 #T #H @(star_ind_l … T H) -T //
+#T #T0 * /2 width=5/
+qed-.
 
-lemma sstas_inv_sort1: ∀h,g,L,U,k. ⦃h, L⦄ ⊢ ⋆k •*[g] U → ∀l. deg h g k l →
-                       U = ⋆((next h)^l k).
-/2 width=6/ qed-.
+(* Basic properties *********************************************************)
 
-fact sstas_inv_bind1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
-                          ∀J,X,Y. T = ⓑ{J}Y.X →
-                          ∃∃Z. ⦃h, L.ⓑ{J}Y⦄ ⊢ X •*[g] Z & U = ⓑ{J}Y.Z.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #U0 #HU0 #J #X #Y #H destruct
-  elim (ssta_inv_bind1 … HU0) -HU0 #X0 #HX0 #H destruct /3 width=3/
-| #T0 #U0 #l #HTU0 #_ #IHU0 #J #X #Y #H destruct
-  elim (ssta_inv_bind1 … HTU0) -HTU0 #X0 #HX0 #H destruct
-  elim (IHU0 J X0 Y ?) -IHU0 // #X1 #HX01 #H destruct /3 width=4/
-]
-qed.
+lemma sstas_refl: ∀h,g,G,L. reflexive … (sstas h g G L).
+// qed.
 
-lemma sstas_inv_bind1: ∀h,g,J,L,Y,X,U. ⦃h, L⦄ ⊢ ⓑ{J}Y.X •*[g] U →
-                       ∃∃Z. ⦃h, L.ⓑ{J}Y⦄ ⊢ X •*[g] Z & U = ⓑ{J}Y.Z.
-/2 width=3/ qed-.
+lemma ssta_sstas: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U⦄ → ⦃G, L⦄ ⊢ T •*[h, g] U.
+/3 width=2 by R_to_star, ex_intro/ qed. (**) (* auto fails without trace *)
 
-fact sstas_inv_appl1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U → ∀X,Y. T = ⓐY.X →
-                          ∃∃Z. ⦃h, L⦄ ⊢ X •*[g] Z & U = ⓐY.Z.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #U0 #HU0 #X #Y #H destruct
-  elim (ssta_inv_appl1 … HU0) -HU0 #X0 #HX0 #H destruct /3 width=3/
-| #T0 #U0 #l #HTU0 #_ #IHU0 #X #Y #H destruct
-  elim (ssta_inv_appl1 … HTU0) -HTU0 #X0 #HX0 #H destruct
-  elim (IHU0 X0 Y ?) -IHU0 // #X1 #HX01 #H destruct /3 width=4/
-]
+lemma sstas_strap1: ∀h,g,G,L,T1,T2,U2,l. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
+                    ⦃G, L⦄ ⊢ T1 •*[h, g] U2.
+/3 width=4 by sstep, ex_intro/ (**) (* auto fails without trace *)
 qed.
 
-lemma sstas_inv_appl1: ∀h,g,L,Y,X,U. ⦃h, L⦄ ⊢ ⓐY.X •*[g] U →
-                       ∃∃Z. ⦃h, L⦄ ⊢ X •*[g] Z & U = ⓐY.Z.
-/2 width=3/ qed-.
+lemma sstas_strap2: ∀h,g,G,L,T1,U1,U2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •*[h, g] U2 →
+                    ⦃G, L⦄ ⊢ T1 •*[h, g] U2.
+/3 width=3 by star_compl, ex_intro/ (**) (* auto fails without trace *)
+qed.
 
-(* Basic forward lemmas *****************************************************)
+(* Basic inversion lemmas ***************************************************)
 
-lemma sstas_fwd_correct: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
-                         ∃∃W. ⦃h, L⦄ ⊢ U •[g, 0] W & ⦃h, L⦄ ⊢ U •*[g] U.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T /2 width=1/ /3 width=2/
+lemma sstas_inv_bind1: ∀h,g,a,I,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓑ{a,I}Y.X •*[h, g] U →
+                       ∃∃Z. ⦃G, L.ⓑ{I}Y⦄ ⊢ X •*[h, g] Z & U = ⓑ{a,I}Y.Z.
+#h #g #a #I #G #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
+#T #U #l #_ #HTU * #Z #HXZ #H destruct
+elim (ssta_inv_bind1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/
 qed-.
 
-(* Basic_1: removed theorems 7:
-            sty1_bind sty1_abbr sty1_appl sty1_cast2
-	    sty1_lift sty1_correct sty1_trans
-*)
+lemma sstas_inv_appl1: ∀h,g,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓐY.X •*[h, g] U →
+                       ∃∃Z. ⦃G, L⦄ ⊢ X •*[h, g] Z & U = ⓐY.Z.
+#h #g #G #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
+#T #U #l #_ #HTU * #Z #HXZ #H destruct
+elim (ssta_inv_appl1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/
+qed-.