matita/matita/contribs/lambdadelta/basic_2A/etc/cny/lpx_cpye.etc

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  14
  15 include "basic_2/substitution/cpye_cpye.ma".
  16 include "basic_2/reduction/lpx_cpys.ma".
  17
  18 axiom cpx_cpys_conf_lpx: ∀h,g,G,d,e.
  19                          ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡[h, g] T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡[h, g] L1 →
  20                          ∀T2. ⦃G, L0⦄ ⊢ T0 ▶*[d, e] T2 →
  21                          ∃∃T. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] T & ⦃G, L0⦄ ⊢ T2 ➡[h, g] T.
  22
  23 (* SN EXTENDED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *********************)
  24
  25 (* Forward lemmas on evaluation for extended substitution *******************)
  26
  27 lemma cpx_cpys_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
  28                              ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
  29                              ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] U1 →
  30                              ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
  31                              ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
  32 #h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e #HTU1
  33 elim (cpx_cpys_conf_lpx … HT12 … HL12 … HTU1) -T1
  34 /3 width=9 by cpx_cpys_trans_lpx, cpye_cpys_conf/
  35 qed-.
  36
  37 lemma cpx_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
  38                         ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
  39                         ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] 𝐍⦃U1⦄ →
  40                         ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
  41                         ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
  42 #h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e *
  43 /2 width=9 by cpx_cpys_cpye_fwd_lpx/
  44 qed-.