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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/unwind/sstas_sstas.ma".
16 include "basic_2/computation/cprs_lfprs.ma".
17 include "basic_2/computation/dxprs.ma".
19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
21 (* Advanced properties ******************************************************)
23 lemma dxprs_cprs_trans: ∀h,g,L,T1,T,T2.
24 ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
25 #h #g #L #T1 #T #T2 * #T0 #HT10 #HT0 #HT2
26 lapply (cprs_trans … HT0 … HT2) -T /2 width=3/
29 lemma sstas_dxprs_trans: ∀h,g,L,T1,T,T2.
30 ⦃h, L⦄ ⊢ T1 •*[g] T → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
31 #h #g #L #T1 #T #T2 #HT1 * #T0 #HT0 #HT02
32 lapply (sstas_trans … HT1 … HT0) -T /2 width=3/
35 (* Advanced inversion lemmas ************************************************)
37 lemma dxprs_inv_abbr_abst: ∀h,g,a1,a2,L,V1,W2,T1,T2. ⦃h, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[g] ⓛ{a2}W2.T2 →
38 ∃∃T. ⦃h, L.ⓓV1⦄ ⊢ T1 •*➡*[g] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
39 #h #g #a1 #a2 #L #V1 #W2 #T1 #T2 * #X #H1 #H2
40 elim (sstas_inv_bind1 … H1) -H1 #U1 #HTU1 #H destruct
41 elim (cprs_inv_abbr1 … H2) -H2 *
42 [ #V2 #U2 #HV12 #HU12 #H destruct