src/HOL/Quotient_Examples/Cset.thy

--- a/src/HOL/Quotient_Examples/Cset.thy	Tue Oct 25 16:09:02 2011 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,102 +0,0 @@
-(*  Title:      HOL/Quotient_Examples/Cset.thy
-    Author:     Florian Haftmann, Alexander Krauss, TU Muenchen
-*)
-
-header {* A variant of theory Cset from Library, defined as a quotient *}
-
-theory Cset
-imports "~~/src/HOL/Library/More_Set" "~~/src/HOL/Library/More_List" "~~/src/HOL/Library/Quotient_Syntax"
-begin
-
-subsection {* Lifting *}
-
-(*FIXME: quotient package requires a dedicated constant*)
-definition set_eq :: "'a set \<Rightarrow> 'a set \<Rightarrow> bool"
-where [simp]: "set_eq \<equiv> op ="
-
-quotient_type 'a set = "'a Set.set" / "set_eq"
-by (simp add: identity_equivp)
-
-hide_type (open) set
-
-subsection {* Operations *}
-
-lemma [quot_respect]:
-  "(op = ===> set_eq ===> op =) (op \<in>) (op \<in>)"
-  "(op = ===> set_eq) Collect Collect"
-  "(set_eq ===> op =) More_Set.is_empty More_Set.is_empty"
-  "(op = ===> set_eq ===> set_eq) Set.insert Set.insert"
-  "(op = ===> set_eq ===> set_eq) More_Set.remove More_Set.remove"
-  "(op = ===> set_eq ===> set_eq) image image"
-  "(op = ===> set_eq ===> set_eq) More_Set.project More_Set.project"
-  "(set_eq ===> op =) Ball Ball"
-  "(set_eq ===> op =) Bex Bex"
-  "(set_eq ===> op =) Finite_Set.card Finite_Set.card"
-  "(set_eq ===> set_eq ===> op =) (op \<subseteq>) (op \<subseteq>)"
-  "(set_eq ===> set_eq ===> op =) (op \<subset>) (op \<subset>)"
-  "(set_eq ===> set_eq ===> set_eq) (op \<inter>) (op \<inter>)"
-  "(set_eq ===> set_eq ===> set_eq) (op \<union>) (op \<union>)"
-  "set_eq {} {}"
-  "set_eq UNIV UNIV"
-  "(set_eq ===> set_eq) uminus uminus"
-  "(set_eq ===> set_eq ===> set_eq) minus minus"
-  "(set_eq ===> op =) Inf Inf"
-  "(set_eq ===> op =) Sup Sup"
-  "(op = ===> set_eq) List.set List.set"
-  "(set_eq ===> (op = ===> set_eq) ===> set_eq) UNION UNION"
-by (auto simp: fun_rel_eq)
-
-quotient_definition "member :: 'a => 'a Cset.set => bool"
-is "op \<in>"
-quotient_definition "Set :: ('a => bool) => 'a Cset.set"
-is Collect
-quotient_definition is_empty where "is_empty :: 'a Cset.set \<Rightarrow> bool"
-is More_Set.is_empty
-quotient_definition insert where "insert :: 'a \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is Set.insert
-quotient_definition remove where "remove :: 'a \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is More_Set.remove
-quotient_definition map where "map :: ('a \<Rightarrow> 'b) \<Rightarrow> 'a Cset.set \<Rightarrow> 'b Cset.set"
-is image
-quotient_definition filter where "filter :: ('a \<Rightarrow> bool) \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is More_Set.project
-quotient_definition "forall :: 'a Cset.set \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"
-is Ball
-quotient_definition "exists :: 'a Cset.set \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"
-is Bex
-quotient_definition card where "card :: 'a Cset.set \<Rightarrow> nat"
-is Finite_Set.card
-quotient_definition set where "set :: 'a list => 'a Cset.set"
-is List.set
-quotient_definition subset where "subset :: 'a Cset.set \<Rightarrow> 'a Cset.set \<Rightarrow> bool"
-is "op \<subseteq> :: 'a set \<Rightarrow> 'a set \<Rightarrow> bool"
-quotient_definition psubset where "psubset :: 'a Cset.set \<Rightarrow> 'a Cset.set \<Rightarrow> bool"
-is "op \<subset> :: 'a set \<Rightarrow> 'a set \<Rightarrow> bool"
-quotient_definition inter where "inter :: 'a Cset.set \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is "op \<inter> :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-quotient_definition union where "union :: 'a Cset.set \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is "op \<union> :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-quotient_definition empty where "empty :: 'a Cset.set"
-is "{} :: 'a set"
-quotient_definition UNIV where "UNIV :: 'a Cset.set"
-is "Set.UNIV :: 'a set"
-quotient_definition uminus where "uminus :: 'a Cset.set \<Rightarrow> 'a Cset.set"
-is "uminus_class.uminus :: 'a set \<Rightarrow> 'a set"
-quotient_definition minus where "minus :: 'a Cset.set \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set"
-is "(op -) :: 'a set \<Rightarrow> 'a set \<Rightarrow> 'a set"
-quotient_definition Inf where "Inf :: ('a :: Inf) Cset.set \<Rightarrow> 'a"
-is "Inf_class.Inf :: ('a :: Inf) set \<Rightarrow> 'a"
-quotient_definition Sup where "Sup :: ('a :: Sup) Cset.set \<Rightarrow> 'a"
-is "Sup_class.Sup :: ('a :: Sup) set \<Rightarrow> 'a"
-quotient_definition UNION where "UNION :: 'a Cset.set \<Rightarrow> ('a \<Rightarrow> 'b Cset.set) \<Rightarrow> 'b Cset.set"
-is "Complete_Lattices.UNION :: 'a set \<Rightarrow> ('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"
-
-hide_const (open) is_empty insert remove map filter forall exists card
-  set subset psubset inter union empty UNIV uminus minus Inf Sup UNION
-
-hide_fact (open) is_empty_def insert_def remove_def map_def filter_def
-  forall_def exists_def card_def set_def subset_def psubset_def
-  inter_def union_def empty_def UNIV_def uminus_def minus_def Inf_def Sup_def
-  UNION_eq
-
-end