matita/matita/contribs/lambda_delta/Basic_2/reducibility/twhnf.ma

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  14
  15 include "Basic_2/grammar/tshf.ma".
  16 include "Basic_2/reducibility/tpr.ma".
  17
  18 (* CONTEXT-FREE WEAK HEAD NORMAL TERMS **************************************)
  19
  20 definition twhnf: predicate term ≝ NF … tpr tshf.
  21
  22 interpretation
  23    "context-free weak head normality (term)"
  24    'WHdNormal T = (twhnf T).
  25
  26 (* Basic inversion lemmas ***************************************************)
  27
  28 lemma twhnf_inv_tshf: ∀T. 𝐖𝐇𝐍[T] → T ≈ T.
  29 normalize /2 width=1/
  30 qed-.
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma tpr_tshf: ∀T1,T2. T1 ➡ T2 → T1 ≈ T1 → T1 ≈ T2.
  35 #T1 #T2 #H elim H -T1 -T2 //
  36 [ #I #V1 #V2 #T1 #T2 #_ #_ #_ #IHT12 #H
  37   elim (tshf_inv_flat1 … H) -H #W2 #U2 #HT1U2 #HT1 #_ #H1 #H2 destruct
  38   lapply (IHT12 HT1U2) -IHT12 -HT1U2 #HUT2
  39   lapply (simple_tshf_repl_dx … HUT2 HT1) /2 width=1/
  40 | #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
  41   elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #H
  42   elim (simple_inv_bind … H)
  43 | #I #V1 #V2 #T1 #T #T2 #_ #_ #_ #_ #_ #H
  44   elim (tshf_inv_bind1 … H) -H #W2 #U2 #H destruct //
  45 | #V2 #V1 #V #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
  46   elim (tshf_inv_flat1 … H) -H #U1 #U2 #_ #H
  47   elim (simple_inv_bind … H)
  48 | #V #T #T1 #T2 #_ #_ #_ #H
  49   elim (tshf_inv_bind1 … H) -H #W2 #U2 #H destruct
  50 | #V #T1 #T2 #_ #_ #H
  51   elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #_ #_ #H destruct
  52 ]
  53 qed.
  54
  55 lemma twhnf_tshf: ∀T. T ≈ T → 𝐖𝐇𝐍[T].
  56 /2 width=1/ qed.