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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_lift.ma".
16 include "basic_2/computation/cprs_lift.ma".
17 include "basic_2/computation/dxprs.ma".
19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
21 (* Advanced inversion lemmas *************************************************)
23 lemma dxprs_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[g] U2 →
24 ∃∃V2,T2. L ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[g] T2 &
26 #h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
27 elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
28 elim (cprs_inv_abst1 Abst V1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
31 (* Advanced properties ******************************************************)
33 lemma ssta_cprs_dxprs: ∀h,g,L,T1,T,T2,l. ⦃h, L⦄ ⊢ T1 •[g, l+1] T →
34 L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
37 (* Relocation properties ****************************************************)
39 lemma dxprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
40 ∀h,g,T2. ⦃h, K⦄ ⊢ T1 •*➡*[g] T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
41 ⦃h, L⦄ ⊢ U1 •*➡*[g] U2.
42 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #T2 * #T
43 elim (lift_total T d e) /3 width=11/
46 lemma dxprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
47 ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •*➡*[g] U2 →
48 ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •*➡*[g] T2.
49 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * #U #HU1 #HU2
50 elim (sstas_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HT1 #HTU
51 elim (cprs_inv_lift1 … HLK … HTU … HU2) -U -L /3 width=5/