Dummy dependent types are no longer cleaned in inductive type arities.

[helm.git] / helm / software / matita / contribs / POPLmark / Fsub / util.ma

diff --git a/helm/software/matita/contribs/POPLmark/Fsub/util.ma b/helm/software/matita/contribs/POPLmark/Fsub/util.ma
index 4f5e1542232f753e7fbb209ecc3fbb0a7ec69760..3521e87ddf7ee1abde19af4ea3154e7003d8adf9 100644 (file)
--- a/helm/software/matita/contribs/POPLmark/Fsub/util.ma
+++ b/helm/software/matita/contribs/POPLmark/Fsub/util.ma
@@ -12,10 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/Fsub/util".
 include "logic/equality.ma".
 include "nat/compare.ma".
 include "list/list.ma".
+include "list/in.ma".
 
 (*** useful definitions and lemmas not really related to Fsub ***)
 
@@ -43,92 +43,15 @@ apply (leb_elim m n)
   ]
 qed.  
 
-inductive in_list (A:Type): A → (list A) → Prop ≝
-| in_Base : ∀ x,l.(in_list A x (x::l))
-| in_Skip : ∀ x,y,l.(in_list A x l) → (in_list A x (y::l)).
-
 notation > "hvbox(x ∈ l)"
   non associative with precedence 30 for @{ 'inlist $x $l }.
 notation < "hvbox(x \nbsp ∈ \nbsp l)"
   non associative with precedence 30 for @{ 'inlist $x $l }.
 interpretation "item in list" 'inlist x l =
-  (cic:/matita/Fsub/util/in_list.ind#xpointer(1/1) _ x l).
-
-definition incl : \forall A.(list A) \to (list A) \to Prop \def
-  \lambda A,l,m.\forall x.(in_list A x l) \to (in_list A x m).               
-              
-(* FIXME: use the map in library/list (when there will be one) *)
-definition map : \forall A,B,f.((list A) \to (list B)) \def
-  \lambda A,B,f.let rec map (l : (list A)) : (list B) \def
-    match l in list return \lambda l0:(list A).(list B) with
-      [nil \Rightarrow (nil B)
-      |(cons (a:A) (t:(list A))) \Rightarrow 
-        (cons B (f a) (map t))] in map.
-
-lemma in_list_nil : \forall A,x.\lnot (in_list A x []).
-intros.unfold.intro.inversion H
-  [intros;lapply (sym_eq ? ? ? H2);destruct Hletin
-  |intros;destruct H4]
-qed.
-
-lemma in_cons_case : ∀A.∀x,h:A.∀t:list A.x ∈ h::t → x = h ∨ (x ∈ t).
-intros;inversion H;intros
-  [destruct H2;left;symmetry;reflexivity
-  |destruct H4;right;applyS H1]
-qed.
-
-lemma append_nil:\forall A:Type.\forall l:list A. l@[]=l.
-intros.
-elim l;intros;autobatch.
-qed.
-
-lemma append_cons:\forall A.\forall a:A.\forall l,l1. 
-l@(a::l1)=(l@[a])@l1.
-intros.
-rewrite > associative_append.
-reflexivity.
-qed.
-
-lemma in_list_append1: \forall A.\forall x:A.
-\forall l1,l2. x \in l1 \to x \in l1@l2.
-intros.
-elim H
-  [simplify.apply in_Base
-  |simplify.apply in_Skip.assumption
-  ]
-qed.
-
-lemma in_list_append2: \forall A.\forall x:A.
-\forall l1,l2. x \in l2 \to x \in l1@l2.
-intros 3.
-elim l1
-  [simplify.assumption
-  |simplify.apply in_Skip.apply H.assumption
-  ]
-qed.
-
-theorem append_to_or_in_list: \forall A:Type.\forall x:A.
-\forall l,l1. x \in l@l1 \to (x \in l) \lor (x \in l1).
-intros 3.
-elim l
-  [right.apply H
-  |simplify in H1.inversion H1;intros; destruct;
-    [left.apply in_Base
-    | elim (H l2)
-      [left.apply in_Skip. assumption
-      |right.assumption
-      |assumption
-      ]
-    ]
-  ]
-qed.
+  (cic:/matita/list/in/in_list.ind#xpointer(1/1) _ x l).
 
 lemma max_case : \forall m,n.(max m n) = match (leb m n) with
       [ true \Rightarrow n
       | false \Rightarrow m ].
 intros;elim m;simplify;reflexivity;
 qed.
-
-lemma incl_A_A: ∀T,A.incl T A A.
-intros.unfold incl.intros.assumption.
-qed.
\ No newline at end of file