1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/unfold/delift_lift.ma".
16 include "basic_2/static/ssta_ssta.ma".
17 include "basic_2/unwind/sstas_lift.ma".
19 (* STRATIFIED UNWIND ON TERMS ***********************************************)
21 (* Advanced inversion lemmas ************************************************)
23 lemma sstas_inv_O: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
24 ∀T0. ⦃h, L⦄ ⊢ T •[g , 0] T0 → U = T.
25 #h #g #L #T #U #H @(sstas_ind_alt … H) -T //
26 #T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
27 elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
30 lemma sstas_inv_S: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
31 ∀T0,l. ⦃h, L⦄ ⊢ T •[g , l+1] T0 → ⦃h, L⦄ ⊢ T0 •*[g] U.
32 #h #g #L #T #U #H @(sstas_ind_alt … H) -T
34 elim (ssta_mono … HUT … HU0) <plus_n_Sm #H destruct
35 | #T0 #U0 #l0 #HTU0 #HU0 #_ #T #l #HT0
36 elim (ssta_mono … HT0 … HTU0) -T0 #_ #H destruct -l0 //
40 (* Main properties **********************************************************)
42 theorem sstas_mono: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
43 ∀U2. ⦃h, L⦄ ⊢ T •*[g] U2 → U1 = U2.
44 #h #g #L #T #U1 #H @(sstas_ind_alt … H) -T
46 >(sstas_inv_O … HU12 … HUT1) -h -L -T1 -U2 //
47 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #U2 #HU12
48 lapply (sstas_inv_S … HU12 … HTU0) -T0 -l0 /2 width=1/
52 (* More advancd inversion lemmas ********************************************)
54 fact sstas_inv_lref1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U → ∀j. T = #j →
55 ∃∃I,K,V,W. ⇩[0, j] L ≡ K. ⓑ{I}V & ⦃h, K⦄ ⊢ V •*[g] W &
56 L ⊢ U ▼*[0, j + 1] ≡ W.
57 #h #g #L #T #U #H @(sstas_ind_alt … H) -T
58 [ #T #HUT #j #H destruct
59 elim (ssta_inv_lref1 … HUT) -HUT * #K #V #W [2: #l] #HLK #HVW #HVT
60 [ <plus_n_Sm #H destruct
63 | #T0 #U0 #l0 #HTU0 #HU0 #_ #j #H destruct
64 elim (ssta_inv_lref1 … HTU0) -HTU0 * #K #V #W [2: #l] #HLK #HVW #HVU0
66 lapply (ldrop_fwd_ldrop2 … HLK) #H
67 elim (sstas_inv_lift1 … HU0 … H … HVU0) -HU0 -H -HVU0 /3 width=7/
68 | elim (sstas_total_S … HVW) -HVW #T #HVT #HWT
69 lapply (ldrop_fwd_ldrop2 … HLK) #H
70 elim (sstas_inv_lift1 … HU0 … H … HVU0) -HU0 -H -HVU0 #X #HWX
71 >(sstas_mono … HWX … HWT) -X -W /3 width=7/