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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 *)
10 (* \ / This file is distributed under the terms of the *)
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15 include "basic_2/unfold/sstas_lift.ma".
16 include "basic_2/computation/cprs_lift.ma".
17 include "basic_2/computation/cpds.ma".
19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
21 (* Relocation properties ****************************************************)
23 lemma cpds_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
24 ∀h,g,T2. ⦃h, K⦄ ⊢ T1 •*➡*[g] T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
25 ⦃h, L⦄ ⊢ U1 •*➡*[g] U2.
26 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #T2 * #T
27 elim (lift_total T d e) /3 width=11/
30 lemma cpds_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
31 ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •*➡*[g] U2 →
32 ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •*➡*[g] T2.
33 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * #U #HU1 #HU2
34 elim (sstas_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HT1 #HTU
35 elim (cprs_inv_lift1 … HU2 … HLK … HTU) -U -L /3 width=5/