matita/matita/contribs/lambdadelta/basic_2/grammar/lenv_length.ma

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  14
  15 include "basic_2/grammar/lenv.ma".
  16
  17 (* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
  18
  19 let rec length L ≝ match L with
  20 [ LAtom       ⇒ 0
  21 | LPair L _ _ ⇒ length L + 1
  22 ].
  23
  24 interpretation "length (local environment)" 'card L = (length L).
  25
  26 (* Basic inversion lemmas ***************************************************)
  27
  28 lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
  29 * // #L #I #V normalize <plus_n_Sm #H destruct
  30 qed-.
  31
  32 lemma length_inv_zero_sn: ∀L. 0 = |L| → L = ⋆.
  33 * // #L #I #V normalize <plus_n_Sm #H destruct
  34 qed-.
  35
  36 lemma length_inv_pos_dx: ∀d,L. |L| = d + 1 →
  37                          ∃∃I,K,V. |K| = d & L = K. ⓑ{I}V.
  38 #d *
  39 [ normalize <plus_n_Sm #H destruct
  40 | #K #I #V #H
  41   lapply (injective_plus_l … H) -H /2 width=5/
  42 ]
  43 qed-.
  44
  45 lemma length_inv_pos_sn: ∀d,L. d + 1 = |L| →
  46                          ∃∃I,K,V. d = |K| & L = K. ⓑ{I}V.
  47 #d *
  48 [ normalize <plus_n_Sm #H destruct
  49 | #K #I #V #H
  50   lapply (injective_plus_l … H) -H /2 width=5/
  51 ]
  52 qed-.