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14
15 include "basic_2/unfold/ltpss_sn_alt.ma".
16 include "basic_2/reducibility/ltpr_ltpss_dx.ma".
17
18 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
19
20 (* Properties on sn parallel unfold on local environments *******************)
21
22 (* Note: this can also be proved like ltpr_ltpss_dx_conf *)
23 lemma ltpr_ltpss_sn_conf: ∀L1,K1,d,e. L1 ⊢ ▶* [d, e] K1 → ∀L2. L1 ➡ L2 →
24                           ∃∃K2. L2 ⊢ ▶* [d, e] K2 & K1 ➡ K2.
25 #L1 #K1 #d #e #H
26 lapply (ltpss_sn_ltpssa … H) -H #H
27 @(ltpssa_ind … H) -K1 /2 width=3/
28 #K #K1 #_ #HK1 #IHK #L2 #HL12
29 elim (IHK … HL12) -L1 #K2 #HLK2 #HK2
30 elim (ltpr_ltpss_dx_conf … HK1 … HK2) -K /3 width=3/
31 qed.