-(**************************************************************************)
-(* ___ *)
-(* ||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/unfold/ltpss_sn_alt.ma".
-include "basic_2/static/ssta_ltpss_dx.ma".
-
-(* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
-
-(* Properties about sn parallel unfold **************************************)
-
-lemma ssta_ltpss_sn_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ →
- ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
- ∃∃U2. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* [d, e] U2.
-#h #g #L1 #T #U1 #l #HTU1 #L2 #d #e #HL12
-lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
-@(ltpssa_ind … HL12) -L2 [ /2 width=3/ ] -HTU1
-#L #L2 #HL1 #HL2 * #U #HTU #HU1
-lapply (ltpssa_ltpss_sn … HL1) -HL1 #HL1
-elim (ssta_ltpss_dx_conf … HTU … HL2) -HTU #U2 #HTU2 #HU2
-lapply (ltpss_dx_tpss_trans_eq … HU2 … HL2) -HU2 -HL2 #HU2
-lapply (ltpss_sn_tpss_trans_eq … HU2 … HL1) -HU2 -HL1 #HU2
-lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
-qed.
-
-lemma ssta_ltpss_sn_tpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
- ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
- ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
- ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ &
- L1 ⊢ U1 ▶* [d, e] U2.
-#h #g #L1 #T1 #U1 #l #HTU1 #L2 #d #e #HL12 #T2 #HT12
-elim (ssta_ltpss_sn_conf … HTU1 … HL12) -HTU1 #U #HT1U #HU1
-elim (ssta_tpss_conf … HT1U … HT12) -T1 #U2 #HTU2 #HU2
-lapply (ltpss_sn_tpss_trans_eq … HU2 … HL12) -HU2 -HL12 #HU2
-lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
-qed.
-
-lemma ssta_ltpss_sn_tps_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
- ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
- ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
- ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ &
- L1 ⊢ U1 ▶* [d, e] U2.
-/3 width=3/ qed.