preservation of stratified vaildity through ordinary reduction and static typing

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / unfold / lsstas_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
index 6fab6dec640d242cc4733df1317062ac093c60a0..849579fa8491b90d6a9df5f410dc3956d74af0a7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/lsstas_alt.ma
@@ -21,9 +21,9 @@ include "basic_2/unfold/lsstas_lift.ma".
 inductive lsstasa (h) (g): genv → relation4 lenv nat term term ≝
 | lsstasa_O   : ∀G,L,T. lsstasa h g G L 0 T T
 | lsstasa_sort: ∀G,L,l,k. lsstasa h g G L l (⋆k) (⋆((next h)^l k))
-| lsstasa_ldef: ∀G,L,K,V,W,U,i,l. ⇩[0, i] L ≡ K.ⓓV → lsstasa h g G K (l+1) V W →
+| lsstasa_ldef: ∀G,L,K,V,W,U,i,l. ⇩[i] L ≡ K.ⓓV → lsstasa h g G K (l+1) V W →
                 ⇧[0, i+1] W ≡ U → lsstasa h g G L (l+1) (#i) U
-| lsstasa_ldec: ∀G,L,K,W,V,U,i,l,l0. ⇩[0, i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
+| lsstasa_ldec: ∀G,L,K,W,V,U,i,l,l0. ⇩[i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
                 lsstasa h g G K l W V → ⇧[0, i+1] V ≡ U → lsstasa h g G L (l+1) (#i) U
 | lsstasa_bind: ∀a,I,G,L,V,T,U,l. lsstasa h g G (L.ⓑ{I}V) l T U →
                 lsstasa h g G L l (ⓑ{a,I}V.T) (ⓑ{a,I}V.U)
@@ -38,7 +38,7 @@ interpretation "nat-iterated stratified static type assignment (term) alternativ
 
 lemma ssta_lsstasa: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •[h, g] U → ⦃G, L⦄ ⊢ T ••*[h, g, 1] U.
 #h #g #G #L #T #U #H elim H -G -L -T -U
-// /2 width=1/ /2 width=6/ /2 width=8/
+/2 width=8 by lsstasa_O, lsstasa_sort, lsstasa_ldef, lsstasa_ldec, lsstasa_bind, lsstasa_appl, lsstasa_cast/
 qed.
 
 lemma lsstasa_step_dx: ∀h,g,G,L,T1,T,l. ⦃G, L⦄ ⊢ T1 ••*[h, g, l] T →
@@ -48,29 +48,29 @@ lemma lsstasa_step_dx: ∀h,g,G,L,T1,T,l. ⦃G, L⦄ ⊢ T1 ••*[h, g, l] T 
 | #G #L #l #k #X #H >(ssta_inv_sort1 … H) -X >commutative_plus //
 | #G #L #K #V #W #U #i #l #HLK #_ #HWU #IHVW #U2 #HU2
   lapply (ldrop_fwd_drop2 … HLK) #H
-  elim (ssta_inv_lift1 … HU2 … H … HWU) -H -U /3 width=6/
+  elim (ssta_inv_lift1 … HU2 … H … HWU) -H -U /3 width=6 by lsstasa_ldef/
 | #G #L #K #W #V #U #i #l #l0 #HLK #HWl0 #_ #HVU #IHWV #U2 #HU2
   lapply (ldrop_fwd_drop2 … HLK) #H
-  elim (ssta_inv_lift1 … HU2 … H … HVU) -H -U /3 width=8/
+  elim (ssta_inv_lift1 … HU2 … H … HVU) -H -U /3 width=8 by lsstasa_ldec/
 | #a #I #G #L #V #T1 #U1 #l #_ #IHTU1 #X #H
-  elim (ssta_inv_bind1 … H) -H #U #HU1 #H destruct /3 width=1/
+  elim (ssta_inv_bind1 … H) -H #U #HU1 #H destruct /3 width=1 by lsstasa_bind/
 | #G #L #V #T1 #U1 #l #_ #IHTU1 #X #H
-  elim (ssta_inv_appl1 … H) -H #U #HU1 #H destruct /3 width=1/
-| /3 width=1/
+  elim (ssta_inv_appl1 … H) -H #U #HU1 #H destruct /3 width=1 by lsstasa_appl/
+| /3 width=1 by lsstasa_cast/
 ]
 qed.
 
 (* Main properties **********************************************************)
 
 theorem lsstas_lsstasa: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T •*[h, g, l] U → ⦃G, L⦄ ⊢ T ••*[h, g, l] U.
-#h #g #G #L #T #U #l #H @(lsstas_ind_dx … H) -U -l // /2 width=3/
+#h #g #G #L #T #U #l #H @(lsstas_ind_dx … H) -U -l /2 width=3 by lsstasa_step_dx, lsstasa_O/
 qed.
 
 (* Main inversion lemmas ****************************************************)
 
 theorem lsstasa_inv_lsstas: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T ••*[h, g, l] U → ⦃G, L⦄ ⊢ T •*[h, g, l] U.
 #h #g #G #L #T #U #l #H elim H -G -L -T -U -l
-// /2 width=1/ /2 width=6/ /3 width=8 by lsstas_ldec, lsstas_inv_SO/
+/2 width=8 by lsstas_inv_SO, lsstas_ldec, lsstas_ldef, lsstas_cast, lsstas_appl, lsstas_bind/
 qed-.
 
 (* Advanced eliminators *****************************************************)
@@ -79,11 +79,11 @@ lemma lsstas_ind_alt: ∀h,g. ∀R:genv→relation4 lenv nat term term.
                       (∀G,L,T. R G L O T T) →
                       (∀G,L,l,k. R G L l (⋆k) (⋆((next h)^l k))) → (
                          ∀G,L,K,V,W,U,i,l.
-                         ⇩[O, i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V •*[h, g, l+1] W → ⇧[O, i+1] W ≡ U →
+                         ⇩[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V •*[h, g, l+1] W → ⇧[O, i+1] W ≡ U →
                          R G K (l+1) V W → R G L (l+1) (#i) U
                       ) → (
                          ∀G,L,K,W,V,U,i,l,l0.
-                         ⇩[O, i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
+                         ⇩[i] L ≡ K.ⓛW → ⦃G, K⦄ ⊢ W ▪[h, g] l0 →
                          ⦃G, K⦄ ⊢ W •*[h, g, l]V → ⇧[O, i+1] V ≡ U →
                          R G K l W V → R G L (l+1) (#i) U
                       ) → (