matita/matita/contribs/lambdadelta/basic_2/reduction/fpn.ma

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  14
  15 include "basic_2/notation/relations/predsn_8.ma".
  16 include "basic_2/grammar/bteq.ma".
  17 include "basic_2/reduction/lpx.ma".
  18
  19 (* ADJACENT "BIG TREE" NORMAL FORMS *****************************************)
  20
  21 definition fpn: ∀h. sd h → tri_relation genv lenv term ≝
  22                 λh,g,G1,L1,T1,G2,L2,T2.
  23                 ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & T1 = T2.
  24
  25 interpretation
  26    "adjacent 'big tree' normal forms (closure)"
  27    'PRedSn h g G1 L1 T1 G2 L2 T2 = (fpn h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic_properties *********************************************************)
  30
  31 lemma fpn_refl: ∀h,g. tri_reflexive … (fpn h g).
  32 /2 width=1 by and3_intro/ qed.
  33
  34 (* Basic forward lemmas *****************************************************)
  35
  36 lemma fpn_fwd_bteq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢➡[h, g] ⦃G2, L2, T2⦄ →
  37                     ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
  38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=4 by lpx_fwd_length, and3_intro/
  39 qed-.