+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/substitution/lpss_ldrop.ma".
-include "basic_2/static/ssta_lift.ma".
-
-(* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
-
-(* Properties about sn parallel substitution ********************************)
-
-(* Note: apparently this was missing in basic_1 *)
-lemma ssta_cpss_lpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
- ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 →
- ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* U2.
-#h #g #L1 #T1 #U1 #l #H elim H -L1 -T1 -U1 -l
-[ #L1 #k1 #l1 #Hkl1 #X #H
- >(cpss_inv_sort1 … H) -H /3 width=3/
-| #L1 #K1 #V1 #W1 #U1 #i #l #HLK1 #_ #HWU1 #IHVW1 #X #H #L2 #HL12
- elim (cpss_inv_lref1 … H) -H
- [ #H destruct
- elim (lpss_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
- elim (lpss_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 #HLK1
- elim (IHVW1 … HV12 … HK12) -IHVW1 -HV12 -HK12 #W2 #HVW2 #HW12
- elim (lift_total W2 0 (i+1)) #U2 #HWU2
- lapply (cpss_lift … HW12 … HLK1 … HWU1 … HWU2) -HW12 -HLK1 -HWU1 /3 width=6/
- | * #Y #Z #V2 #H #HV12 #HV2
- lapply (ldrop_mono … H … HLK1) -H #H destruct
- elim (lpss_ldrop_conf … HLK1 … HL12) -HL12 #Z #H #HLK2
- elim (lpss_inv_pair1 … H) -H #K2 #V0 #HK12 #_ #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK2) -V0 #HLK2
- lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 #HLK1
- elim (IHVW1 … HV12 … HK12) -IHVW1 -HK12 -HV12 #W2 #HVW2 #HW12
- elim (lift_total W2 0 (i+1)) #U2 #HWU2
- lapply (ssta_lift … HVW2 … HLK2 … HV2 … HWU2) -HVW2 -HLK2 -HV2
- lapply (cpss_lift … HW12 … HLK1 … HWU1 … HWU2) -HW12 -HLK1 -HWU1 -HWU2 /3 width=3/
- ]
-| #L1 #K1 #W1 #V1 #U1 #i #l #HLK1 #_ #HWU1 #IHWV1 #X #H #L2 #HL12
- elim (cpss_inv_lref1 … H) -H [ | -IHWV1 -HWU1 -HL12 ]
- [ #H destruct
- elim (lpss_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
- elim (lpss_inv_pair1 … H) -H #K2 #W2 #HK12 #HW12 #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 #HLK1
- elim (IHWV1 … HW12 … HK12) -IHWV1 -HK12 #V2 #HWV2 #_
- elim (lift_total W2 0 (i+1)) #U2 #HWU2
- lapply (cpss_lift … HW12 … HLK1 … HWU1 … HWU2) -HW12 -HLK1 -HWU1 /3 width=6/
- | * #K2 #V2 #W2 #HLK2 #_ #_
- lapply (ldrop_mono … HLK2 … HLK1) -HLK1 -HLK2 #H destruct
- ]
-| #a #I #L1 #V1 #T1 #U1 #l #_ #IHTU1 #X #H #L2 #HL12
- elim (cpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
- elim (IHTU1 … HT12 (L2.ⓑ{I}V2)) -IHTU1 -HT12 /2 width=1/ -HL12 /3 width=5/
-| #L1 #V1 #T1 #U1 #l #_ #IHTU1 #X #H #L2 #HL12
- elim (cpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
- elim (IHTU1 … HT12 … HL12) -IHTU1 -HT12 -HL12 /3 width=5/
-| #L1 #W1 #T1 #U1 #l #_ #IHTU1 #X #H #L2 #HL12
- elim (cpss_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct
- elim (IHTU1 … HT12 … HL12) -IHTU1 -HT12 -HL12 /3 width=3/
-]
-qed-.
-
-lemma ssta_cpss_conf: ∀h,g,L,T1,U1,l. ⦃h, L⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
- ∀T2. L ⊢ T1 ▶* T2 →
- ∃∃U2. ⦃h, L⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L ⊢ U1 ▶* U2.
-/2 width=3 by ssta_cpss_lpss_conf/ qed-.
-
-lemma ssta_lpss_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ →
- ∀L2. L1 ⊢ ▶* L2 →
- ∃∃U2. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* U2.
-/2 width=3 by ssta_cpss_lpss_conf/ qed-.