matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/lpxs_cpye.etc

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  14
  15 include "basic_2/substitution/cpye_lift.ma".
  16 include "basic_2/reduction/lpx_cpye.ma".
  17 include "basic_2/computation/cpxs_cpxs.ma".
  18 include "basic_2/computation/lpxs.ma".
  19
  20 (* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************)
  21
  22 (* Forward lemmas on evaluation for extended substitution *******************)
  23
  24 lemma cpx_cpye_fwd_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 →
  25                          ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
  26                          ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] 𝐍⦃U1⦄ →
  27                          ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
  28                          ⦃G, L1⦄ ⊢ U1 ➡*[h, g] U2.
  29 #h #g #G #L1 #L2 #H @(lpxs_ind_dx … H) -L1
  30 [ /3 width=9 by cpx_cpxs, cpx_cpye_fwd_lpx/
  31 | #L1 #L #HL1 #_ #IHL2 #T1 #T2 #HT12 #U1 #d #e #HTU1 #U2 #HTU2
  32   elim (cpye_total G L T2 d e) #X2 #HTX2
  33   lapply (cpx_cpye_fwd_lpx … HT12 … HL1 … HTU1 … HTX2) -T1
  34   /4 width=9 by lpx_cpxs_trans, cpxs_strap2/ (**) (* full auto too long: 41s *)
  35 ]
  36 qed-.