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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/unfold/ltpss_ltpss.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
20 (* Properties concerning partial unfold on local environments ***************)
22 lemma ltpss_cpr_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
23 ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
24 #L1 #L2 #d #e #HL12 #T1 #T2 *
25 lapply (ltpss_weak_all … HL12)
26 >(ltpss_fwd_length … HL12) -HL12 #HL12 #T #HT1 #HT2
27 elim (ltpss_tpss_conf … HT2 … HL12) -L1 #T0 #HT0 #HT20
28 @(cprs_div … T0) /3 width=3/ (**) (* /4/ is too slow *)
31 lemma ltpss_cprs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
32 ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
33 #L1 #L2 #d #e #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
35 @(cpcs_trans … IHT1) -T1 /2 width=5/
38 lemma ltpss_cpcs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
39 ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
40 #L1 #L2 #d #e #HL12 #T1 #T2 #H
41 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
42 @(cpcs_canc_dx … T) /2 width=5/