matita/matita/contribs/lambdadelta/basic_2A/etc/fpn/fpn.etc

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  14
  15 include "basic_2/notation/relations/btpredsn_8.ma".
  16 include "basic_2/relocation/lleq.ma".
  17 include "basic_2/reduction/lpx.ma".
  18
  19 (* REDUCTION FOR "BIG TREE" NORMAL FORMS ************************************)
  20
  21 inductive fpn (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
  22 | fpn_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → L1 ⋕[T] L2 → fpn h g G L1 T G L2 T
  23 .
  24
  25 interpretation
  26    "reduction for 'big tree' normal forms (closure)"
  27    'BTPRedSn 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 fpn_intro/ qed.
  33
  34 (* Basic inversion lemmas ***************************************************)
  35
  36 lemma fpn_inv_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄ →
  37                    ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & L1 ⋕[T1] L2 & T1 = T2.
  38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
  39 qed-.