update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / list.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma
index 0ea6ae2856d4f3c128a59af277b3674002280315..07e13ea8f8fb361746b45b600cd02e5c0291f556 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/list.ma
@@ -14,7 +14,7 @@
 
 include "ground_2/notation/constructors/circledE_1.ma".
 include "ground_2/notation/constructors/oplusright_3.ma".
-include "ground_2/lib/arith.ma".
+include "ground_2/lib/relations.ma".
 
 (* LISTS ********************************************************************)
 
@@ -26,43 +26,8 @@ interpretation "nil (list)" 'CircledE A = (nil A).
 
 interpretation "cons (list)" 'OPlusRight A hd tl = (cons A hd tl).
 
-rec definition length A (l:list A) on l ≝ match l with
-[ nil      ⇒ 0
-| cons _ l ⇒ ↑(length A l)
-].
-
-interpretation "length (list)"
-   'card l = (length ? l).
-
 rec definition all A (R:predicate A) (l:list A) on l ≝
   match l with
   [ nil        ⇒ ⊤
-  | cons hd tl ⇒ R hd ∧ all A R tl
+  | cons hd tl ⇒ ∧∧ R hd & all A R tl
   ].
-
-(* Basic properties on length ***********************************************)
-
-lemma length_nil (A:Type[0]): |nil A| = 0.
-// qed.
-
-lemma length_cons (A:Type[0]) (l:list A) (a:A): |a⨮l| = ↑|l|.
-// qed.
-
-(* Basic inversion lemmas on length *****************************************)
-
-lemma length_inv_zero_dx (A:Type[0]) (l:list A): |l| = 0 → l = Ⓔ.
-#A * // #a #l >length_cons #H destruct
-qed-.
-
-lemma length_inv_zero_sn (A:Type[0]) (l:list A): 0 = |l| → l = Ⓔ.
-/2 width=1 by length_inv_zero_dx/ qed-.
-
-lemma length_inv_succ_dx (A:Type[0]) (l:list A) (x): |l| = ↑x →
-                         ∃∃tl,a. x = |tl| & l = a ⨮ tl.
-#A * /2 width=4 by ex2_2_intro/
->length_nil #x #H destruct
-qed-.
-
-lemma length_inv_succ_sn (A:Type[0]) (l:list A) (x): ↑x = |l| →
-                         ∃∃tl,a. x = |tl| & l = a ⨮ tl.
-/2 width=1 by length_inv_succ_dx/ qed.