+++ /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/dynamic/snv.ma".
-
-(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
-
-(* Properties on stratified static type assignment for terms ****************)
-
-lemma snv_ssta: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃∃U,l. ⦃h, L⦄ ⊢ T •[g, l] U.
-#h #g #L #T #H elim H -L -T
-[ #L #k elim (deg_total h g k) /3 width=3/
-| * #L #K #V #i #HLK #_ * #W #l0 #HVW
- [ elim (lift_total W 0 (i+1)) /3 width=8/
- | elim (lift_total V 0 (i+1)) /3 width=8/
- ]
-| #a #I #L #V #T #_ #_ #_ * /3 width=3/
-| #a #L #V #W #W1 #T0 #T1 #l #_ #_ #_ #_ #_ #_ * /3 width=3/
-| #L #W #T #U #l #_ #_ #HTU #_ #_ #_ /3 width=3/ (**) (* auto fails without the last #_ *)
-]
-qed-.
-
-fact snv_ssta_conf_aux: ∀h,g,L,T. (
- ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
- ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
- #{L0, T0} < #{L, T} → ⦃h, L0⦄ ⊩ U0 :[g]
- ) →
- ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
- ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
- L0 = L → T0 = T → ⦃h, L0⦄ ⊩ U0 :[g].
-#h #g #L #T #IH1 #L0 #T0 * -L0 -T0
-[
-|
-|
-| #a #L0 #V #W #W0 #T0 #V0 #l0 #HV #HT0 #HVW #HW0 #HTV0 #X #l #H #H1 #H2 destruct
- elim (ssta_inv_appl1 … H) -H #U0 #HTU0 #H destruct
- lapply (IH1 … HT0 … HTU0 ?) // #HU0
- @(snv_appl … HV HU0 HVW HW0) -HV -HU0 -HVW -HW0
-| #L0 #W #T0 #W0 #l0 #_ #HT0 #_ #_ #U0 #l #H #H1 #H2 destruct -W0
- lapply (ssta_inv_cast1 … H) -H /2 width=5/