syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / lenv_length.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
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+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
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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 "static_2/syntax/lenv.ma".
+
+(* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
+
+rec definition length L ≝ match L with
+[ LAtom     ⇒ 0
+| LBind L _ ⇒ ↑(length L)
+].
+
+interpretation "length (local environment)" 'card L = (length L).
+
+(* Basic properties *********************************************************)
+
+lemma length_atom: |⋆| = 0.
+// qed.
+
+(* Basic_2A1: uses: length_pair *)
+lemma length_bind: ∀I,L. |L.ⓘ{I}| = ↑|L|.
+// qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
+* // #L #I >length_bind
+#H destruct
+qed-.
+
+lemma length_inv_zero_sn: ∀L. 0 = |L| → L = ⋆.
+/2 width=1 by length_inv_zero_dx/ qed-.
+
+(* Basic_2A1: was: length_inv_pos_dx *)
+lemma length_inv_succ_dx: ∀n,L. |L| = ↑n →
+                          ∃∃I,K. |K| = n & L = K. ⓘ{I}.
+#n *
+[ >length_atom #H destruct
+| #L #I >length_bind /3 width=4 by ex2_2_intro, injective_S/
+]
+qed-.
+
+(* Basic_2A1: was: length_inv_pos_sn *)
+lemma length_inv_succ_sn: ∀n,L. ↑n = |L| →
+                          ∃∃I,K. n = |K| & L = K. ⓘ{I}.
+#n #L #H lapply (sym_eq ??? H) -H 
+#H elim (length_inv_succ_dx … H) -H /2 width=4 by ex2_2_intro/
+qed-.
+
+(* Basic_2A1: removed theorems 1: length_inj *)