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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground_2/ynat/ynat_lt.ma".
16 include "basic_2/grammar/lenv.ma".
18 (* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
20 let rec length L ≝ match L with
22 | LPair L _ _ ⇒ ⫯(length L)
25 interpretation "length (local environment)" 'card L = (length L).
27 (* Basic properties *********************************************************)
29 lemma length_atom: |⋆| = 0.
32 lemma length_pair: ∀I,L,V. |L.ⓑ{I}V| = ⫯|L|.
35 lemma length_inj: ∀L. |L| < ∞.
36 #L elim L -L /2 width=1 by ylt_succ_Y/
39 (* Basic inversion lemmas ***************************************************)
41 lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
42 * // #L #I #V >length_pair
43 #H elim (ysucc_inv_O_dx … H)
46 lemma length_inv_zero_sn: ∀L. yinj 0 = |L| → L = ⋆.
47 /2 width=1 by length_inv_zero_dx/ qed-.
49 lemma length_inv_pos_dx: ∀l,L. |L| = ⫯l →
50 ∃∃I,K,V. |K| = l & L = K. ⓑ{I}V.
51 #l * /3 width=5 by ysucc_inj, ex2_3_intro/
52 >length_atom #H elim (ysucc_inv_O_sn … H)
55 lemma length_inv_pos_sn: ∀l,L. ⫯l = |L| →
56 ∃∃I,K,V. l = |K| & L = K. ⓑ{I}V.
57 #l #L #H lapply (sym_eq ??? H) -H
58 #H elim (length_inv_pos_dx … H) -H /2 width=5 by ex2_3_intro/