- degree assignment, static type assignment, iterated static type

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / sstas / sstas_sstas.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_sstas.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_sstas.etc
index 2f7e261b409668c3833bf8656ef6b41d0fb1dbee..cc98d0ea05a5899c3e1aba46a94478a737c7defa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_sstas.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_sstas.etc
@@ -12,63 +12,43 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/delift_lift.ma".
 include "basic_2/static/ssta_ssta.ma".
-include "basic_2/unwind/sstas_lift.ma".
+include "basic_2/unfold/sstas.ma".
 
-(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
+(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma sstas_inv_O: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
-                   ∀T0. ⦃h, L⦄ ⊢ T •[g , 0] T0 → U = T.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T //
+lemma sstas_inv_O: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
+                   ∀T0. ⦃G, L⦄ ⊢ T •[h, g] ⦃0, T0⦄ → U = T.
+#h #g #G #L #T #U #H @(sstas_ind_dx … H) -T //
 #T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
 elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
 qed-.
 
-lemma sstas_inv_S: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
-                   ∀T0,l. ⦃h, L⦄ ⊢ T •[g , l+1] T0 → ⦃h, L⦄ ⊢ T0 •*[g] U.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #U0 #HU0 #T #l #HUT
-  elim (ssta_mono … HUT … HU0) <plus_n_Sm #H destruct
-| #T0 #U0 #l0 #HTU0 #HU0 #_ #T #l #HT0
-  elim (ssta_mono … HT0 … HTU0) -T0 #_ #H destruct -l0 //
-]
-qed-.
-
-(* Main properties **********************************************************)
+(* Advanced properties ******************************************************)
 
-theorem sstas_mono: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
-                    ∀U2. ⦃h, L⦄ ⊢ T •*[g] U2 → U1 = U2.
-#h #g #L #T #U1 #H @(sstas_ind_alt … H) -T
-[ #T1 #HUT1 #U2 #HU12
-  >(sstas_inv_O … HU12 … HUT1) -h -L -T1 -U2 //
-| #T0 #U0 #l0 #HTU0 #_ #IHU01 #U2 #HU12
-  lapply (sstas_inv_S … HU12 … HTU0) -T0 -l0 /2 width=1/
-]
+lemma sstas_strip: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+                   ∀U2,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U2⦄ →
+                   T = U1 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#T #U #l0 #HTU #HU1 #_ #U2 #l #H2
+elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
 qed-.
 
-(* More advancd inversion lemmas ********************************************)
+(* Main properties **********************************************************)
 
-fact sstas_inv_lref1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U → ∀j. T = #j →
-                          ∃∃I,K,V,W. ⇩[0, j] L ≡ K. ⓑ{I}V & ⦃h, K⦄ ⊢ V •*[g] W &
-                                     L ⊢ ▼*[0, j + 1] U ≡ W.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #T #HUT #j #H destruct
-  elim (ssta_inv_lref1 … HUT) -HUT * #K #V #W [2: #l] #HLK #HVW #HVT
-  [ <plus_n_Sm #H destruct
-  | /3 width=12/
-  ]
-| #T0 #U0 #l0 #HTU0 #HU0 #_ #j #H destruct
-  elim (ssta_inv_lref1 … HTU0) -HTU0 * #K #V #W [2: #l] #HLK #HVW #HVU0
-  [ #_ -HVW
-    lapply (ldrop_fwd_ldrop2 … HLK) #H
-    elim (sstas_inv_lift1 … HU0 … H … HVU0) -HU0 -H -HVU0 /3 width=7/
-  | elim (sstas_total_S … HVW) -HVW #T #HVT #HWT
-    lapply (ldrop_fwd_ldrop2 … HLK) #H
-    elim (sstas_inv_lift1 … HU0 … H … HVU0) -HU0 -H -HVU0 #X #HWX
-    >(sstas_mono … HWX … HWT) -X -W /3 width=7/
-  ]
+theorem sstas_trans: ∀h,g,G,L,T1,U. ⦃G, L⦄ ⊢ T1 •*[h, g] U →
+                     ∀T2. ⦃G, L⦄ ⊢ U •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*[h, g] T2.
+/2 width=3/ qed-.
+
+theorem sstas_conf: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+                    ∀U2. ⦃G, L⦄ ⊢ T •*[h, g] U2 →
+                   ⦃G, L⦄ ⊢ U1 •*[h, g] U2 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#T #U #l #HTU #HU1 #IHU1 #U2 #H2
+elim (sstas_strip … H2 … HTU) #H destruct
+[ -H2 -IHU1 /3 width=4/
+| -T /2 width=1/
 ]
 qed-.