partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / ssta.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/ssta.ma b/matita/matita/contribs/lambdadelta/basic_2/static/ssta.ma
index d7a32e928b65916c34cef0f7acc8af685c68b81a..9421d7436bfc65b81f28ab726d6cd3e0700d7e44 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/ssta.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/ssta.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/ldrop.ma".
-include "basic_2/unfold/frsups.ma".
+include "basic_2/notation/relations/statictype_6.ma".
+include "basic_2/relocation/ldrop.ma".
 include "basic_2/static/sd.ma".
 
 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
@@ -35,11 +35,11 @@ interpretation "stratified static type assignment (term)"
    'StaticType h g L T U l = (ssta h g l L T U).
 
 definition ssta_step: ∀h. sd h → lenv → relation term ≝ λh,g,L,T,U.
-                      ∃l. ⦃h, L⦄ ⊢ T •[g] ⦃l+1, U⦄.
+                      ∃l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U⦄.
 
 (* Basic inversion lemmas ************************************************)
 
-fact ssta_inv_sort1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ∀k0. T = ⋆k0 →
+fact ssta_inv_sort1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ → ∀k0. T = ⋆k0 →
                          deg h g k0 l ∧ U = ⋆(next h k0).
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #Hkl #k0 #H destruct /2 width=1/
@@ -51,15 +51,15 @@ fact ssta_inv_sort1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 qed.
 
 (* Basic_1: was just: sty0_gen_sort *)
-lemma ssta_inv_sort1: ∀h,g,L,U,k,l. ⦃h, L⦄ ⊢ ⋆k •[g] ⦃l, U⦄ →
+lemma ssta_inv_sort1: ∀h,g,L,U,k,l. ⦃G, L⦄ ⊢ ⋆k •[h, g] ⦃l, U⦄ →
                       deg h g k l ∧ U = ⋆(next h k).
 /2 width=4/ qed-.
 
-fact ssta_inv_lref1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ∀j. T = #j →
-                         (∃∃K,V,W. ⇩[0, j] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V •[g] ⦃l, W⦄ &
+fact ssta_inv_lref1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ → ∀j. T = #j →
+                         (∃∃K,V,W. ⇩[0, j] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V •[h, g] ⦃l, W⦄ &
                                    ⇧[0, j + 1] W ≡ U
                          ) ∨
-                         (∃∃K,W,V,l0. ⇩[0, j] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W •[g] ⦃l0, V⦄ &
+                         (∃∃K,W,V,l0. ⇩[0, j] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W •[h, g] ⦃l0, V⦄ &
                                       ⇧[0, j + 1] W ≡ U & l = l0 + 1
                          ).
 #h #g #L #T #U #l * -L -T -U -l
@@ -73,16 +73,16 @@ fact ssta_inv_lref1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 qed.
 
 (* Basic_1: was just: sty0_gen_lref *)
-lemma ssta_inv_lref1: ∀h,g,L,U,i,l. ⦃h, L⦄ ⊢ #i •[g] ⦃l, U⦄ →
-                      (∃∃K,V,W. ⇩[0, i] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V •[g] ⦃l, W⦄ &
+lemma ssta_inv_lref1: ∀h,g,L,U,i,l. ⦃G, L⦄ ⊢ #i •[h, g] ⦃l, U⦄ →
+                      (∃∃K,V,W. ⇩[0, i] L ≡ K. ⓓV & ⦃h, K⦄ ⊢ V •[h, g] ⦃l, W⦄ &
                                 ⇧[0, i + 1] W ≡ U
                       ) ∨
-                      (∃∃K,W,V,l0. ⇩[0, i] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W •[g] ⦃l0, V⦄ &
+                      (∃∃K,W,V,l0. ⇩[0, i] L ≡ K. ⓛW & ⦃h, K⦄ ⊢ W •[h, g] ⦃l0, V⦄ &
                                    ⇧[0, i + 1] W ≡ U & l = l0 + 1
                       ).
 /2 width=3/ qed-.
 
-fact ssta_inv_gref1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ∀p0. T = §p0 → ⊥.
+fact ssta_inv_gref1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ → ∀p0. T = §p0 → ⊥.
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #_ #p0 #H destruct
 | #L #K #V #W #U #i #l #_ #_ #_ #p0 #H destruct
@@ -92,12 +92,12 @@ fact ssta_inv_gref1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 | #L #W #T #U #l #_ #p0 #H destruct
 qed.
 
-lemma ssta_inv_gref1: ∀h,g,L,U,p,l. ⦃h, L⦄ ⊢ §p •[g] ⦃l, U⦄ → ⊥.
+lemma ssta_inv_gref1: ∀h,g,L,U,p,l. ⦃G, L⦄ ⊢ §p •[h, g] ⦃l, U⦄ → ⊥.
 /2 width=9/ qed-.
 
-fact ssta_inv_bind1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
+fact ssta_inv_bind1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ →
                          ∀a,I,X,Y. T = ⓑ{a,I}Y.X →
-                         ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •[g] ⦃l, Z⦄ & U = ⓑ{a,I}Y.Z.
+                         ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •[h, g] ⦃l, Z⦄ & U = ⓑ{a,I}Y.Z.
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #_ #a #I #X #Y #H destruct
 | #L #K #V #W #U #i #l #_ #_ #_ #a #I #X #Y #H destruct
@@ -109,12 +109,12 @@ fact ssta_inv_bind1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 qed.
 
 (* Basic_1: was just: sty0_gen_bind *)
-lemma ssta_inv_bind1: ∀h,g,a,I,L,Y,X,U,l. ⦃h, L⦄ ⊢ ⓑ{a,I}Y.X •[g] ⦃l, U⦄ →
-                      ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •[g] ⦃l, Z⦄ & U = ⓑ{a,I}Y.Z.
+lemma ssta_inv_bind1: ∀h,g,a,I,L,Y,X,U,l. ⦃G, L⦄ ⊢ ⓑ{a,I}Y.X •[h, g] ⦃l, U⦄ →
+                      ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •[h, g] ⦃l, Z⦄ & U = ⓑ{a,I}Y.Z.
 /2 width=3/ qed-.
 
-fact ssta_inv_appl1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ∀X,Y. T = ⓐY.X →
-                         ∃∃Z. ⦃h, L⦄ ⊢ X •[g] ⦃l, Z⦄ & U = ⓐY.Z.
+fact ssta_inv_appl1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ → ∀X,Y. T = ⓐY.X →
+                         ∃∃Z. ⦃G, L⦄ ⊢ X •[h, g] ⦃l, Z⦄ & U = ⓐY.Z.
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #_ #X #Y #H destruct
 | #L #K #V #W #U #i #l #_ #_ #_ #X #Y #H destruct
@@ -126,12 +126,12 @@ fact ssta_inv_appl1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 qed.
 
 (* Basic_1: was just: sty0_gen_appl *)
-lemma ssta_inv_appl1: ∀h,g,L,Y,X,U,l. ⦃h, L⦄ ⊢ ⓐY.X •[g] ⦃l, U⦄ →
-                      ∃∃Z. ⦃h, L⦄ ⊢ X •[g] ⦃l, Z⦄ & U = ⓐY.Z.
+lemma ssta_inv_appl1: ∀h,g,L,Y,X,U,l. ⦃G, L⦄ ⊢ ⓐY.X •[h, g] ⦃l, U⦄ →
+                      ∃∃Z. ⦃G, L⦄ ⊢ X •[h, g] ⦃l, Z⦄ & U = ⓐY.Z.
 /2 width=3/ qed-.
 
-fact ssta_inv_cast1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
-                         ∀X,Y. T = ⓝY.X → ⦃h, L⦄ ⊢ X •[g] ⦃l, U⦄.
+fact ssta_inv_cast1_aux: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ →
+                         ∀X,Y. T = ⓝY.X → ⦃G, L⦄ ⊢ X •[h, g] ⦃l, U⦄.
 #h #g #L #T #U #l * -L -T -U -l
 [ #L #k #l #_ #X #Y #H destruct
 | #L #K #V #W #U #l #i #_ #_ #_ #X #Y #H destruct
@@ -143,58 +143,6 @@ fact ssta_inv_cast1_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
 qed.
 
 (* Basic_1: was just: sty0_gen_cast *)
-lemma ssta_inv_cast1: ∀h,g,L,X,Y,U,l. ⦃h, L⦄ ⊢ ⓝY.X •[g] ⦃l, U⦄ →
-                      ⦃h, L⦄ ⊢ X •[g] ⦃l, U⦄.
+lemma ssta_inv_cast1: ∀h,g,L,X,Y,U,l. ⦃G, L⦄ ⊢ ⓝY.X •[h, g] ⦃l, U⦄ →
+                      ⦃G, L⦄ ⊢ X •[h, g] ⦃l, U⦄.
 /2 width=4/ qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma ssta_inv_frsupp: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ⦃L, U⦄ ⧁+ ⦃L, T⦄ → ⊥.
-#h #g #L #T #U #l #H elim H -L -T -U -l
-[ #L #k #l #_ #H
-  elim (frsupp_inv_atom1_frsups … H)
-| #L #K #V #W #U #i #l #_ #_ #HWU #_ #H
-  elim (lift_frsupp_trans … (⋆) … H … HWU) -U #X #H
-  elim (lift_inv_lref2_be … H ? ?) -H //
-| #L #K #W #V #U #i #l #_ #_ #HWU #_ #H
-  elim (lift_frsupp_trans … (⋆) … H … HWU) -U #X #H
-  elim (lift_inv_lref2_be … H ? ?) -H //
-| #a #I #L #V #T #U #l #_ #IHTU #H
-  elim (frsupp_inv_bind1_frsups … H) -H #H [2: /4 width=4/ ] -IHTU
-  lapply (frsups_fwd_fw … H) -H normalize
-  <associative_plus <associative_plus #H
-  elim (le_plus_xySz_x_false … H)
-| #L #V #T #U #l #_ #IHTU #H
-  elim (frsupp_inv_flat1_frsups … H) -H #H [2: /4 width=4/ ] -IHTU
-  lapply (frsups_fwd_fw … H) -H normalize
-  <associative_plus <associative_plus #H
-  elim (le_plus_xySz_x_false … H)
-| /3 width=4/
-]
-qed-.
-
-fact ssta_inv_refl_aux: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → T = U → ⊥.
-#h #g #L #T #U #l #H elim H -L -T -U -l
-[ #L #k #l #_ #H
-  lapply (next_lt h k) destruct -H -e0 (**) (* destruct: these premises are not erased *)
-  <e1 -e1 #H elim (lt_refl_false … H)
-| #L #K #V #W #U #i #l #_ #_ #HWU #_ #H destruct
-  elim (lift_inv_lref2_be … HWU ? ?) -HWU //
-| #L #K #W #V #U #i #l #_ #_ #HWU #_ #H destruct
-  elim (lift_inv_lref2_be … HWU ? ?) -HWU //
-| #a #I #L #V #T #U #l #_ #IHTU #H destruct /2 width=1/
-| #L #V #T #U #l #_ #IHTU #H destruct /2 width=1/
-| #L #W #T #U #l #HTU #_ #H destruct
-  elim (ssta_inv_frsupp … HTU ?) -HTU /2 width=1/
-]
-qed-.
-
-lemma ssta_inv_refl: ∀h,g,T,L,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, T⦄ → ⊥.
-/2 width=8 by ssta_inv_refl_aux/ qed-.
-
-lemma ssta_inv_frsups: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → ⦃L, U⦄ ⧁* ⦃L, T⦄ → ⊥.
-#h #g #L #T #U #L #HTU #H elim (frsups_inv_all … H) -H
-[ * #_ #H destruct /2 width=6 by ssta_inv_refl/
-| /2 width=8 by ssta_inv_frsupp/
-]
-qed-.