matita/matita/contribs/lambdadelta/basic_2A/grammar/lenv_length.ma

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  14
  15 include "ground_2/xoa/ex_2_3.ma".
  16 include "basic_2A/grammar/lenv.ma".
  17
  18 (* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
  19
  20 let rec length L ≝ match L with
  21 [ LAtom       ⇒ 0
  22 | LPair L _ _ ⇒ length L + 1
  23 ].
  24
  25 interpretation "length (local environment)" 'card L = (length L).
  26
  27 (* Basic inversion lemmas ***************************************************)
  28
  29 lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
  30 * // #L #I #V normalize <plus_n_Sm #H destruct
  31 qed-.
  32
  33 lemma length_inv_zero_sn: ∀L. 0 = |L| → L = ⋆.
  34 * // #L #I #V normalize <plus_n_Sm #H destruct
  35 qed-.
  36
  37 lemma length_inv_pos_dx: ∀l,L. |L| = l + 1 →
  38                          ∃∃I,K,V. |K| = l & L = K. ⓑ{I}V.
  39 #l *
  40 [ normalize <plus_n_Sm #H destruct
  41 | #K #I #V #H
  42   lapply (injective_plus_l … H) -H /2 width=5 by ex2_3_intro/
  43 ]
  44 qed-.
  45
  46 lemma length_inv_pos_sn: ∀l,L. l + 1 = |L| →
  47                          ∃∃I,K,V. l = |K| & L = K. ⓑ{I}V.
  48 #l *
  49 [ normalize <plus_n_Sm #H destruct
  50 | #K #I #V #H
  51   lapply (injective_plus_l … H) -H /2 width=5 by ex2_3_intro/
  52 ]
  53 qed-.