matita/matita/contribs/lambdadelta/basic_2/etc/cpys/lpys_lpys.etc

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  14
  15 include "basic_2/substitution/cpys_cpys.ma".
  16
  17 (* SN EXTENDED MULTIPLE SUBSTITUTION FOR LOCAL ENVIRONMENTS *****************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem lpys_trans: ∀G. Transitive … (lpys G).
  22 /3 width=5 by lpx_sn_trans, cpys_trans_lpys/
  23 qed-.
  24
  25 (* Advanced forward lemmas **************************************************)
  26
  27 lemma cpys_fwd_shift1_ext: ∀G,L1,L,T1,T. ⦃G, L⦄ ⊢ L1 @@ T1 ▶*× T →
  28                            ∃∃L2,T2. ⦃G, L @@ L1⦄ ⊢ ▶*× L @@ L2 & ⦃G, L @@ L1⦄ ⊢ T1 ▶*× T2 &
  29                                     T = L2 @@ T2.
  30 #G #L1 @(lenv_ind_dx … L1) -L1
  31 [ #L #T1 #T #HT1 @ex3_2_intro
  32   [3: // |4,5: // |1,2: skip ] (**) (* auto does not work *)
  33 | #I #L1 #V1 #IH #L #T1 #T >shift_append_assoc #H <append_assoc
  34   elim (cpys_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
  35   elim (IH … HT12) -IH -HT12 #L2 #T #HL12 #HT1 #H destruct
  36   lapply (lpys_trans … HL12 (L.ⓑ{I}V2@@L2) ?) -HL12 /3 width=1 by lpys_append, lpys_pair/ #HL12
  37   @(ex3_2_intro … (⋆.ⓑ{I}V2@@L2)) [4: /2 width=3 by trans_eq/ | skip ] <append_assoc // (**) (* explicit constructor *)
  38 ]
  39 qed-.