matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltpr_ltpss_sn.etc

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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.