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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_computation/lprs_cpms.ma".
16 include "basic_2/rt_equivalence/cpes_cpms.ma".
18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
20 (* Advanced forward lemmas **************************************************)
22 lemma cpes_fwd_abst_bi (h) (n1) (n2) (p1) (p2) (G) (L):
23 ∀W1,W2,T1,T2. ❨G,L❩ ⊢ ⓛ[p1]W1.T1 ⬌*[h,n1,n2] ⓛ[p2]W2.T2 →
24 ∧∧ p1 = p2 & ❨G,L❩ ⊢ W1 ⬌*[h,0,O] W2.
25 #h #n1 #n2 #p1 #p2 #G #L #W1 #W2 #T1 #T2 * #X #H1 #H2
26 elim (cpms_inv_abst_sn … H1) #W0 #X0 #HW10 #_ #H destruct
27 elim (cpms_inv_abst_bi … H2) #H #HW20 #_ destruct
28 /3 width=3 by cpms_div, conj/
31 (* Main properties **********************************************************)
33 theorem cpes_cpes_trans (h) (n1) (n2) (G) (L) (T):
34 ∀T1. ❨G,L❩ ⊢ T ⬌*[h,n1,0] T1 →
35 ∀T2. ❨G,L❩ ⊢ T1 ⬌*[h,0,n2] T2 → ❨G,L❩ ⊢ T ⬌*[h,n1,n2] T2.
36 #h #n1 #n2 #G #L #T #T1 #HT1 #T2 * #X #HX1 #HX2
37 lapply (cpes_cprs_trans … HT1 … HX1) -T1 #HTX
38 lapply (cpes_cpms_div … HTX … HX2) -X //