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/rt_computation/cprs_cprs.ma".
16 include "basic_2/rt_equivalence/cpes.ma".
18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
20 (* Properties with t-bound rt-computation on terms **************************)
22 lemma cpes_cprs_trans (h) (n) (G) (L) (T0):
23 ∀T1. ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T0 →
24 ∀T2. ❪G,L❫ ⊢ T0 ➡*[h,0] T2 → ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T2.
25 #h #n #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT02
26 elim (cprs_conf … HT0 … HT02) -T0 #T0 #HT0 #HT20
27 /3 width=3 by cpms_div, cpms_cprs_trans/
30 lemma cpes_cpms_div (h) (n) (n1) (n2) (G) (L) (T0):
31 ∀T1. ❪G,L❫ ⊢ T1 ⬌*[h,n,n1] T0 →
32 ∀T2. ❪G,L❫ ⊢ T2 ➡*[h,n2] T0 → ❪G,L❫ ⊢ T1 ⬌*[h,n,n2+n1] T2.
33 #h #n #n1 #n2 #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT20
34 lapply (cpms_trans … HT20 … HT0) -T0 #HT2
35 /2 width=3 by cpms_div/