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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/rt_transition/cpt_cpm.ma".
16 include "basic_2/rt_computation/cpms_cpms.ma".
17 include "basic_2/rt_computation/cpts.ma".
19 (* T-BOUND CONTEXT-SENSITIVE PARALLEL T-COMPUTATION FOR TERMS ***************)
21 (* Forward lemmas with t-bound rt-computation for terms *********************)
23 lemma cpts_fwd_cpms (h) (n) (G) (L):
24 ∀T1,T2. ❨G,L❩ ⊢ T1 ⬆*[h,n] T2 → ❨G,L❩ ⊢ T1 ➡*[h,n] T2.
25 #h #n #G #L #T1 #T2 #H
26 @(cpts_ind_dx … H) -n -T2 [ // ]
27 #n1 #n2 #T #T2 #_ #IH #HT2
28 /3 width=3 by cpms_step_dx, cpt_fwd_cpm/
31 lemma cpts_cprs_trans (h) (n) (G) (L) (T):
32 ∀T1. ❨G,L❩ ⊢ T1 ⬆*[h,n] T →
33 ∀T2. ❨G,L❩ ⊢ T ➡*[h,0] T2 → ❨G,L❩ ⊢ T1 ➡*[h,n] T2.
34 #h #n #G #L #T #T1 #HT1 #T2 #HT2
35 /3 width=3 by cpts_fwd_cpms, cpms_cprs_trans/ qed-.