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+chapter \<open>Generated by Lem from map.lem.\<close>
+
+theory "Lem_map"
+
+imports
+ Main
+ "Lem_bool"
+ "Lem_basic_classes"
+ "Lem_function"
+ "Lem_maybe"
+ "Lem_list"
+ "Lem_tuple"
+ "Lem_set"
+ "Lem_num"
+
+begin
+
+
+
+(*open import Bool Basic_classes Function Maybe List Tuple Set Num*)
+(*open import {hol} `finite_mapTheory` `finite_mapLib`*)
+
+(*type map 'k 'v*)
+
+
+
+(* -------------------------------------------------------------------------- *)
+(* Map equality. *)
+(* -------------------------------------------------------------------------- *)
+
+(*val mapEqual : forall 'k 'v. Eq 'k, Eq 'v => map 'k 'v -> map 'k 'v -> bool*)
+(*val mapEqualBy : forall 'k 'v. ('k -> 'k -> bool) -> ('v -> 'v -> bool) -> map 'k 'v -> map 'k 'v -> bool*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* Map type class *)
+(* -------------------------------------------------------------------------- *)
+
+(*class ( MapKeyType 'a )
+ val {ocaml;coq} mapKeyCompare : 'a -> 'a -> ordering
+end*)
+
+(* -------------------------------------------------------------------------- *)
+(* Empty maps *)
+(* -------------------------------------------------------------------------- *)
+
+(*val empty : forall 'k 'v. MapKeyType 'k => map 'k 'v*)
+(*val emptyBy : forall 'k 'v. ('k -> 'k -> ordering) -> map 'k 'v*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* Insertion *)
+(* -------------------------------------------------------------------------- *)
+
+(*val insert : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v -> map 'k 'v*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* Singleton *)
+(* -------------------------------------------------------------------------- *)
+
+(*val singleton : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v*)
+
+
+
+(* -------------------------------------------------------------------------- *)
+(* Emptyness check *)
+(* -------------------------------------------------------------------------- *)
+
+(*val null : forall 'k 'v. MapKeyType 'k, Eq 'k, Eq 'v => map 'k 'v -> bool*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* lookup *)
+(* -------------------------------------------------------------------------- *)
+
+(*val lookupBy : forall 'k 'v. ('k -> 'k -> ordering) -> 'k -> map 'k 'v -> maybe 'v*)
+
+(*val lookup : forall 'k 'v. MapKeyType 'k => 'k -> map 'k 'v -> maybe 'v*)
+
+(* -------------------------------------------------------------------------- *)
+(* findWithDefault *)
+(* -------------------------------------------------------------------------- *)
+
+(*val findWithDefault : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v -> 'v*)
+
+(* -------------------------------------------------------------------------- *)
+(* from lists *)
+(* -------------------------------------------------------------------------- *)
+
+(*val fromList : forall 'k 'v. MapKeyType 'k => list ('k * 'v) -> map 'k 'v*)
+(*let fromList l= foldl (fun m (k,v) -> insert k v m) empty l*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* to sets / domain / range *)
+(* -------------------------------------------------------------------------- *)
+
+(*val toSet : forall 'k 'v. MapKeyType 'k, SetType 'k, SetType 'v => map 'k 'v -> set ('k * 'v)*)
+(*val toSetBy : forall 'k 'v. (('k * 'v) -> ('k * 'v) -> ordering) -> map 'k 'v -> set ('k * 'v)*)
+
+
+(*val domainBy : forall 'k 'v. ('k -> 'k -> ordering) -> map 'k 'v -> set 'k*)
+(*val domain : forall 'k 'v. MapKeyType 'k, SetType 'k => map 'k 'v -> set 'k*)
+
+
+(*val range : forall 'k 'v. MapKeyType 'k, SetType 'v => map 'k 'v -> set 'v*)
+(*val rangeBy : forall 'k 'v. ('v -> 'v -> ordering) -> map 'k 'v -> set 'v*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* member *)
+(* -------------------------------------------------------------------------- *)
+
+(*val member : forall 'k 'v. MapKeyType 'k, SetType 'k, Eq 'k => 'k -> map 'k 'v -> bool*)
+
+(*val notMember : forall 'k 'v. MapKeyType 'k, SetType 'k, Eq 'k => 'k -> map 'k 'v -> bool*)
+
+(* -------------------------------------------------------------------------- *)
+(* Quantification *)
+(* -------------------------------------------------------------------------- *)
+
+(*val any : forall 'k 'v. MapKeyType 'k, Eq 'v => ('k -> 'v -> bool) -> map 'k 'v -> bool*)
+(*val all : forall 'k 'v. MapKeyType 'k, Eq 'v => ('k -> 'v -> bool) -> map 'k 'v -> bool*)
+
+(*let all P m= (forall k v. (P k v && ((Instance_Basic_classes_Eq_Maybe_maybe.=) (lookup k m) (Just v))))*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* Set-like operations. *)
+(* -------------------------------------------------------------------------- *)
+(*val deleteBy : forall 'k 'v. ('k -> 'k -> ordering) -> 'k -> map 'k 'v -> map 'k 'v*)
+(*val delete : forall 'k 'v. MapKeyType 'k => 'k -> map 'k 'v -> map 'k 'v*)
+(*val deleteSwap : forall 'k 'v. MapKeyType 'k => map 'k 'v -> 'k -> map 'k 'v*)
+
+(*val union : forall 'k 'v. MapKeyType 'k => map 'k 'v -> map 'k 'v -> map 'k 'v*)
+
+(*val unions : forall 'k 'v. MapKeyType 'k => list (map 'k 'v) -> map 'k 'v*)
+
+
+(* -------------------------------------------------------------------------- *)
+(* Maps (in the functor sense). *)
+(* -------------------------------------------------------------------------- *)
+
+(*val map : forall 'k 'v 'w. MapKeyType 'k => ('v -> 'w) -> map 'k 'v -> map 'k 'w*)
+
+(*val mapi : forall 'k 'v 'w. MapKeyType 'k => ('k -> 'v -> 'w) -> map 'k 'v -> map 'k 'w*)
+
+(* -------------------------------------------------------------------------- *)
+(* Cardinality *)
+(* -------------------------------------------------------------------------- *)
+(*val size : forall 'k 'v. MapKeyType 'k, SetType 'k => map 'k 'v -> nat*)
+
+(* instance of SetType *)
+definition map_setElemCompare :: "(('d*'c)set \<Rightarrow>('b*'a)set \<Rightarrow> 'e)\<Rightarrow>('d,'c)Map.map \<Rightarrow>('b,'a)Map.map \<Rightarrow> 'e " where
+ " map_setElemCompare cmp x y = (
+ cmp (map_to_set x) (map_to_set y))"
+
+end