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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/pconvstar_7.ma".
16 include "basic_2/rt_computation/cpms.ma".
18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
20 (* Basic_2A1: uses: scpes *)
21 definition cpes (h) (n1) (n2): relation4 genv lenv term term ≝
23 ∃∃T. ❨G,L❩ ⊢ T1 ➡*[h,n1] T & ❨G,L❩ ⊢ T2 ➡*[h,n2] T.
25 interpretation "t-bound context-sensitive parallel rt-equivalence (term)"
26 'PConvStar h n1 n2 G L T1 T2 = (cpes h n1 n2 G L T1 T2).
28 (* Basic properties *********************************************************)
30 (* Basic_2A1: uses: scpds_div *)
31 lemma cpms_div (h) (n1) (n2):
32 ∀G,L,T1,T. ❨G,L❩ ⊢ T1 ➡*[h,n1] T →
33 ∀T2. ❨G,L❩ ⊢ T2 ➡*[h,n2] T → ❨G,L❩ ⊢ T1 ⬌*[h,n1,n2] T2.
34 /2 width=3 by ex2_intro/ qed.
36 lemma cpes_refl (h): ∀G,L. reflexive … (cpes h 0 0 G L).
37 /2 width=3 by cpms_div/ qed.
39 (* Basic_2A1: uses: scpes_sym *)
40 lemma cpes_sym (h) (n1) (n2):
41 ∀G,L,T1,T2. ❨G,L❩ ⊢ T1 ⬌*[h,n1,n2] T2 → ❨G,L❩ ⊢ T2 ⬌*[h,n2,n1] T1.
42 #h #n1 #n2 #G #L #T1 #T2 * /2 width=3 by cpms_div/