- degree assignment, static type assignment, iterated static type

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc
index 838c7b6d4a4ee168dbef83d03e88e34e3a390015..ec6fdc0c3253d733bec705657b1c9b3c418a53df 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc
@@ -13,45 +13,40 @@
 (**************************************************************************)
 
 include "basic_2/static/ssta_lift.ma".
-include "basic_2/unwind/sstas.ma".
+include "basic_2/unfold/sstas.ma".
 
-(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
+(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
 
-(* Advanced properties ******************************************************)
+(* Advanced forward lemmas **************************************************)
 
-lemma sstas_total_S: ∀h,g,L,l,T,U. ⦃h, L⦄ ⊢ T•[g, l + 1]U →
-                     ∃∃W. ⦃h, L⦄ ⊢ T •*[g] W & ⦃h, L⦄ ⊢ U •*[g] W.
-#h #g #L #l @(nat_ind_plus … l) -l
-[ #T #U #HTU
-  elim (ssta_fwd_correct … HTU) /4 width=4/
-| #l #IHl #T #U #HTU
-  elim (ssta_fwd_correct … HTU) <minus_plus_m_m #V #HUV
-  elim (IHl … HUV) -IHl -HUV /3 width=4/
-]
+lemma sstas_fwd_correct: ∀h,g,G,L,T1,U1,l1. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l1, U1⦄ →
+                         ∀T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 →
+                         ∃∃U2,l2. ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l2, U2⦄.
+#h #g #G #L #T1 #U1 #l1 #HTU1 #T2 #H @(sstas_ind … H) -T2 [ /2 width=3/ ] -HTU1
+#T #T2 #l #_ #HT2 * #U #l0 #_ -l0
+elim (ssta_fwd_correct … HT2) -T /2 width=3/
 qed-.
 
 (* Properties on relocation *************************************************)
 
-lemma sstas_lift: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
+lemma sstas_lift: ∀h,g,G,L1,T1,U1. ⦃G, L1⦄ ⊢ T1 •*[h, g] U1 →
                   ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
-                  ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •*[g] U2.
-#h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
-[ #T1 #HUT1 #L2 #d #e #HL21 #X #HX #U2 #HU12
-  >(lift_mono … HX … HU12) -X
-  elim (lift_total T1 d e) /3 width=10/
+                  ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃G, L2⦄ ⊢ T2 •*[h, g] U2.
+#h #g #G #L1 #T1 #U1 #H @(sstas_ind_dx … H) -T1
+[ #L2 #d #e #HL21 #X #HX #U2 #HU12
+  >(lift_mono … HX … HU12) -X //
 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL21 #T2 #HT02 #U2 #HU12
   elim (lift_total U0 d e) /3 width=10/
 ]
 qed.
 
-lemma sstas_inv_lift1: ∀h,g,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 →
+(* Inversion lemmas on relocation *******************************************)
+
+lemma sstas_inv_lift1: ∀h,g,G,L2,T2,U2. ⦃G, L2⦄ ⊢ T2 •*[h, g] U2 →
                        ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
-                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 & ⇧[d, e] U1 ≡ U2.
-#h #g #L2 #T2 #U2 #H @(sstas_ind_alt … H) -T2
-[ #T2 #HUT2 #L1 #d #e #HL21 #U1 #HU12
-  elim (ssta_inv_lift1 … HUT2 … HL21 … HU12) -HUT2 -HL21 /3 width=3/
-| #T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
-  elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
-  elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
-]
+                       ∃∃U1. ⦃G, L1⦄ ⊢ T1 •*[h, g] U1 & ⇧[d, e] U1 ≡ U2.
+#h #g #G #L2 #T2 #U2 #H @(sstas_ind_dx … H) -T2 /2 width=3/
+#T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
+elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
+elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
 qed-.