+++ /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/unfold/delift_lift.ma".
-include "basic_2/static/ssta_ssta.ma".
-include "basic_2/unwind/sstas_lift.ma".
-
-(* STRATIFIED UNWIND ON 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 //
-#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 **********************************************************)
-
-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/
-]
-qed-.
-
-(* More advancd inversion lemmas ********************************************)
-
-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/
- ]
-]
-qed-.