matita/matita/contribs/lambdadelta/basic_2A/etc/cpys2/cpx_cpys.etc

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  14
  15 include "basic_2/substitution/cpys_alt.ma".
  16 include "basic_2/reduction/cpx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
  19
  20 (* Properties on local environment refinement for extended substitution *****)
  21
  22 lemma lsuby_cpx_trans: ∀h,g,G. lsub_trans … (cpx h g G) (lsuby 0 (∞)).
  23 #h #g #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
  24 [ //
  25 | /2 width=2 by cpx_sort/
  26 | #I #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
  27   elim (lsuby_ldrop_trans_be … HL12 … HLK1) // -HL12 -HLK1 /3 width=7 by cpx_delta/
  28 |4,9: /4 width=1 by cpx_bind, cpx_beta, lsuby_pair_O_Y/
  29 |5,7,8: /3 width=1 by cpx_flat, cpx_tau, cpx_ti/
  30 |6,10: /4 width=3 by cpx_zeta, cpx_theta, lsuby_pair_O_Y/
  31 ]
  32 qed-.
  33
  34 (* Properties on context-sensitive extended multiple substitution for terms *)
  35
  36 lemma cpys_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
  37 #h #g #G #L #T1 #T2 #d #e #H @(cpys_ind_alt … H) -G -L -T1 -T2 -d -e
  38 /2 width=7 by cpx_delta, cpx_bind, cpx_flat/
  39 qed.
  40
  41 lemma cpy_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
  42 /3 width=3 by cpy_cpys, cpys_cpx/ qed.