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

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  14
  15 include "basic_2/reducibility/cpr_ltpr.ma".
  16 include "basic_2/computation/cprs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties concerning parallel unfold on terms ***************************)
  21
  22 (* Basic_1: was only: pr3_subst1 *)
  23 lemma cprs_tpss_ltpr: ∀L1,T1,U1,d,e. L1 ⊢ T1 ▶* [d, e] U1 →
  24                       ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 →
  25                       ∃∃U2. L2 ⊢ U1 ➡* U2 & L2 ⊢ T2 ▶* [d, e] U2.
  26 #L1 #T1 #U1 #d #e #HTU1 #L2 #HL12 #T2 #HT12 elim HT12 -T2
  27 [ #T2 #HT12
  28   elim (cpr_tpss_ltpr … HL12 … HT12 … HTU1) -L1 -T1 /3 width=3/
  29 | #T #T2 #_ #HT2 * #U #HU1 #HTU
  30   elim (cpr_tpss_ltpr … HT2 … HTU) -L1 -T // /3 width=3/
  31 ]
  32 qed.