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15 include "basic_2/equivalence/cpcs_ltpss_dx.ma".
17 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
19 (* Properties concerning sn partial unfold on local environments ************)
21 lemma cpcs_ltpss_sn_conf: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
22 ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
24 lapply (ltpss_sn_ltpssa … H) -H #H @(ltpssa_ind … H) -L2 //
25 #L #L2 #_ #HL2 #IHL1 #T1 #U1 #HTU1
26 lapply (IHL1 … HTU1) -IHL1 -HTU1 #HTU1
27 lapply (cpcs_ltpss_dx_conf … HL2 … HTU1) -HTU1 -HL2 //