renaming ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_new / lenv / lenv_length.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lenv/lenv_length.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/lenv/lenv_length.etc
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--- a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lenv/lenv_length.etc
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "ground_2/ynat/ynat_lt.ma".
-include "basic_2/grammar/lenv.ma".
-
-(* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
-
-let rec length L ≝ match L with
-[ LAtom       ⇒ 0
-| LPair L _ _ ⇒ ⫯(length L)
-].
-
-interpretation "length (local environment)" 'card L = (length L).
-
-(* Basic properties *********************************************************)
-
-lemma length_atom: |⋆| = 0.
-// qed.
-
-lemma length_pair: ∀I,L,V. |L.ⓑ{I}V| = ⫯|L|.
-// qed.
-
-lemma length_inj: ∀L. |L| < ∞.
-#L elim L -L /2 width=1 by ylt_succ_Y/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
-* // #L #I #V >length_pair
-#H elim (ysucc_inv_O_dx … H)
-qed-.
-
-lemma length_inv_zero_sn: ∀L. yinj 0 = |L| → L = ⋆.
-/2 width=1 by length_inv_zero_dx/ qed-.
-
-lemma length_inv_pos_dx: ∀l,L. |L| = ⫯l →
-                         ∃∃I,K,V. |K| = l & L = K. ⓑ{I}V.
-#l * /3 width=5 by ysucc_inj, ex2_3_intro/
->length_atom #H elim (ysucc_inv_O_sn … H)
-qed-.
-
-lemma length_inv_pos_sn: ∀l,L. ⫯l = |L| →
-                         ∃∃I,K,V. l = |K| & L = K. ⓑ{I}V.
-#l #L #H lapply (sym_eq ??? H) -H 
-#H elim (length_inv_pos_dx … H) -H /2 width=5 by ex2_3_intro/
-qed-.