matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr_ltpss_dx.etc

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  14
  15 include "basic_2/reducibility/ltpr_tpss.ma".
  16
  17 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
  18
  19 (* Properties concerning dx parallel unfold on local environments ***********)
  20
  21 lemma ltpr_ltpss_dx_conf: ∀L1,K1,d,e. L1 ▶* [d, e] K1 → ∀L2. L1 ➡ L2 →
  22                           ∃∃K2. L2 ▶* [d, e] K2 & K1 ➡ K2.
  23 #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
  24 [ /2 width=3/
  25 | #L1 #I #V1 #X #H
  26   elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct /3 width=5/
  27 | #L1 #K1 #I #V1 #W1 #e #_ #HVW1 #IHLK1 #X #H
  28   elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
  29   elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
  30   elim (ltpr_tpr_tpss_conf … HK12 … HV12 … HVW1) -V1 /3 width=5/
  31 | #L1 #K1 #I #V1 #W1 #d #e #_ #HVW1 #IHLK1 #X #H
  32   elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
  33   elim (IHLK1 … HL12) -L1 #K2 #HLK2 #HK12
  34   elim (ltpr_tpr_tpss_conf … HK12 … HV12 … HVW1) -V1 /3 width=5/
  35 ]
  36 qed.