lambda finaly moved in lib

[helm.git] / matita / matita / contribs / lambda / terms / multiplicity.ma

diff --git a/matita/matita/contribs/lambda/terms/multiplicity.ma b/matita/matita/contribs/lambda/terms/multiplicity.ma
deleted file mode 100644 (file)
index 4f41b75..0000000
--- a/matita/matita/contribs/lambda/terms/multiplicity.ma
+++ /dev/null
@@ -1,52 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "terms/relocating_substitution.ma".
-
-(* MULTIPLICITY *************************************************************)
-
-(* Note: this gives the number of variable references in M *)
-let rec mult M on M ≝ match M with
-[ VRef i   ⇒ 1
-| Abst A   ⇒ mult A
-| Appl B A ⇒ (mult B) + (mult A)
-].
-
-interpretation "term multiplicity"
-   'Multiplicity M = (mult M).
-
-notation "hvbox( ♯{ term 46 M } )"
-   non associative with precedence 90
-   for @{ 'Multiplicity $M }.
-
-lemma mult_positive: ∀M. 0 < ♯{M}.
-#M elim M -M // /2 width=1/
-qed.
-
-lemma mult_lift: ∀h,M,d. ♯{↑[d, h] M} = ♯{M}.
-#h #M elim M -M normalize //
-qed.
-
-theorem mult_dsubst: ∀D,M,d. ♯{[d ↙ D] M} ≤ ♯{M} * ♯{D}.
-#D #M elim M -M
-[ #i #d elim (lt_or_eq_or_gt i d) #Hid
-  [ >(dsubst_vref_lt … Hid) normalize //
-  | destruct >dsubst_vref_eq normalize //
-  | >(dsubst_vref_gt … Hid) normalize //
-  ]
-| normalize //
-| normalize #B #A #IHB #IHA #d
-  >distributive_times_plus_r /2 width=1/
-]
-qed.