# HG changeset patch
# User wenzelm
# Date 1001622360 -7200
# Node ID c760ea8154ee81fad2b76d331e37f5262f1efb3d
# Parent  c7e1db87b98a51240dc8dbc3f68618c3a3b19064
renamed theory "subset" to "Typedef";

diff -r c7e1db87b98a -r c760ea8154ee src/HOL/Tools/typedef_package.ML
--- a/src/HOL/Tools/typedef_package.ML	Thu Sep 27 22:25:12 2001 +0200
+++ b/src/HOL/Tools/typedef_package.ML	Thu Sep 27 22:26:00 2001 +0200
@@ -28,7 +28,7 @@
 
 (** theory context references **)
 
-val type_definitionN = "subset.type_definition";
+val type_definitionN = "Typedef.type_definition";
 val type_definition_def = thm "type_definition_def";
 
 val Rep = thm "Rep";
@@ -98,7 +98,7 @@
 
 fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
   let
-    val _ = Theory.requires thy "subset" "typedefs";
+    val _ = Theory.requires thy "Typedef" "typedefs";
     val sign = Theory.sign_of thy;
     val full = Sign.full_name sign;
 
diff -r c7e1db87b98a -r c760ea8154ee src/HOL/Typedef.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Typedef.thy	Thu Sep 27 22:26:00 2001 +0200
@@ -0,0 +1,139 @@
+(*  Title:      HOL/Typedef.thy
+    ID:         $Id$
+    Author:     Markus Wenzel, TU Munich
+
+Misc set-theory lemmas and HOL type definitions.
+*)
+
+theory Typedef = Set
+files "subset.ML" "equalities.ML" "mono.ML"
+  "Tools/induct_attrib.ML" ("Tools/typedef_package.ML"):
+
+(** belongs to theory Ord **)
+  
+theorems linorder_cases [case_names less equal greater] =
+  linorder_less_split
+
+(* Courtesy of Stephan Merz *)
+lemma Least_mono: 
+  "mono (f::'a::order => 'b::order) ==> EX x:S. ALL y:S. x <= y
+    ==> (LEAST y. y : f ` S) = f (LEAST x. x : S)"
+  apply clarify
+  apply (erule_tac P = "%x. x : S" in LeastI2)
+   apply fast
+  apply (rule LeastI2)
+  apply (auto elim: monoD intro!: order_antisym)
+  done
+
+
+(*belongs to theory Set*)
+setup Rulify.setup
+
+
+section {* HOL type definitions *}
+
+constdefs
+  type_definition :: "('a => 'b) => ('b => 'a) => 'b set => bool"
+  "type_definition Rep Abs A ==
+    (\<forall>x. Rep x \<in> A) \<and>
+    (\<forall>x. Abs (Rep x) = x) \<and>
+    (\<forall>y \<in> A. Rep (Abs y) = y)"
+  -- {* This will be stated as an axiom for each typedef! *}
+
+lemma type_definitionI [intro]:
+  "(!!x. Rep x \<in> A) ==>
+    (!!x. Abs (Rep x) = x) ==>
+    (!!y. y \<in> A ==> Rep (Abs y) = y) ==>
+    type_definition Rep Abs A"
+  by (unfold type_definition_def) blast
+
+theorem Rep: "type_definition Rep Abs A ==> Rep x \<in> A"
+  by (unfold type_definition_def) blast
+
+theorem Rep_inverse: "type_definition Rep Abs A ==> Abs (Rep x) = x"
+  by (unfold type_definition_def) blast
+
+theorem Abs_inverse: "type_definition Rep Abs A ==> y \<in> A ==> Rep (Abs y) = y"
+  by (unfold type_definition_def) blast
+
+theorem Rep_inject: "type_definition Rep Abs A ==> (Rep x = Rep y) = (x = y)"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  show ?thesis
+  proof
+    assume "Rep x = Rep y"
+    hence "Abs (Rep x) = Abs (Rep y)" by (simp only:)
+    thus "x = y" by (simp only: Rep_inverse [OF tydef])
+  next
+    assume "x = y"
+    thus "Rep x = Rep y" by simp
+  qed
+qed
+
+theorem Abs_inject:
+  "type_definition Rep Abs A ==> x \<in> A ==> y \<in> A ==> (Abs x = Abs y) = (x = y)"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  assume x: "x \<in> A" and y: "y \<in> A"
+  show ?thesis
+  proof
+    assume "Abs x = Abs y"
+    hence "Rep (Abs x) = Rep (Abs y)" by simp
+    moreover from x have "Rep (Abs x) = x" by (rule Abs_inverse [OF tydef])
+    moreover from y have "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
+    ultimately show "x = y" by (simp only:)
+  next
+    assume "x = y"
+    thus "Abs x = Abs y" by simp
+  qed
+qed
+
+theorem Rep_cases:
+  "type_definition Rep Abs A ==> y \<in> A ==> (!!x. y = Rep x ==> P) ==> P"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  assume y: "y \<in> A" and r: "(!!x. y = Rep x ==> P)"
+  show P
+  proof (rule r)
+    from y have "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
+    thus "y = Rep (Abs y)" ..
+  qed
+qed
+
+theorem Abs_cases:
+  "type_definition Rep Abs A ==> (!!y. x = Abs y ==> y \<in> A ==> P) ==> P"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  assume r: "!!y. x = Abs y ==> y \<in> A ==> P"
+  show P
+  proof (rule r)
+    have "Abs (Rep x) = x" by (rule Rep_inverse [OF tydef])
+    thus "x = Abs (Rep x)" ..
+    show "Rep x \<in> A" by (rule Rep [OF tydef])
+  qed
+qed
+
+theorem Rep_induct:
+  "type_definition Rep Abs A ==> y \<in> A ==> (!!x. P (Rep x)) ==> P y"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  assume "!!x. P (Rep x)" hence "P (Rep (Abs y))" .
+  moreover assume "y \<in> A" hence "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
+  ultimately show "P y" by (simp only:)
+qed
+
+theorem Abs_induct:
+  "type_definition Rep Abs A ==> (!!y. y \<in> A ==> P (Abs y)) ==> P x"
+proof -
+  assume tydef: "type_definition Rep Abs A"
+  assume r: "!!y. y \<in> A ==> P (Abs y)"
+  have "Rep x \<in> A" by (rule Rep [OF tydef])
+  hence "P (Abs (Rep x))" by (rule r)
+  moreover have "Abs (Rep x) = x" by (rule Rep_inverse [OF tydef])
+  ultimately show "P x" by (simp only:)
+qed
+
+setup InductAttrib.setup
+use "Tools/typedef_package.ML"
+
+end
diff -r c7e1db87b98a -r c760ea8154ee src/HOL/subset.thy
--- a/src/HOL/subset.thy	Thu Sep 27 22:25:12 2001 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,139 +0,0 @@
-(*  Title:      HOL/subset.thy
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1994  University of Cambridge
-
-Subset lemmas and HOL type definitions.
-*)
-
-theory subset = Set
-files "Tools/induct_attrib.ML" ("Tools/typedef_package.ML"):
-
-(** belongs to theory Ord **)
-  
-theorems linorder_cases [case_names less equal greater] =
-  linorder_less_split
-
-(* Courtesy of Stephan Merz *)
-lemma Least_mono: 
-"[| mono (f::'a::order => 'b::order); EX x:S. ALL y:S. x <= y |]  
-   ==> (LEAST y. y : f`S) = f(LEAST x. x : S)"
-apply clarify
-apply (erule_tac P = "%x. x : S" in LeastI2)
-apply  fast
-apply (rule LeastI2)
-apply (auto elim: monoD intro!: order_antisym)
-done
-
-
-(*belongs to theory Set*)
-setup Rulify.setup
-
-
-section {* HOL type definitions *}
-
-constdefs
-  type_definition :: "('a => 'b) => ('b => 'a) => 'b set => bool"
-  "type_definition Rep Abs A ==
-    (\\<forall>x. Rep x \\<in> A) \\<and>
-    (\\<forall>x. Abs (Rep x) = x) \\<and>
-    (\\<forall>y \\<in> A. Rep (Abs y) = y)"
-  -- {* This will be stated as an axiom for each typedef! *}
-
-lemma type_definitionI [intro]:
-  "(!!x. Rep x \\<in> A) ==>
-    (!!x. Abs (Rep x) = x) ==>
-    (!!y. y \\<in> A ==> Rep (Abs y) = y) ==>
-    type_definition Rep Abs A"
-  by (unfold type_definition_def) blast
-
-theorem Rep: "type_definition Rep Abs A ==> Rep x \\<in> A"
-  by (unfold type_definition_def) blast
-
-theorem Rep_inverse: "type_definition Rep Abs A ==> Abs (Rep x) = x"
-  by (unfold type_definition_def) blast
-
-theorem Abs_inverse: "type_definition Rep Abs A ==> y \\<in> A ==> Rep (Abs y) = y"
-  by (unfold type_definition_def) blast
-
-theorem Rep_inject: "type_definition Rep Abs A ==> (Rep x = Rep y) = (x = y)"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  show ?thesis
-  proof
-    assume "Rep x = Rep y"
-    hence "Abs (Rep x) = Abs (Rep y)" by (simp only:)
-    thus "x = y" by (simp only: Rep_inverse [OF tydef])
-  next
-    assume "x = y"
-    thus "Rep x = Rep y" by simp
-  qed
-qed
-
-theorem Abs_inject:
-  "type_definition Rep Abs A ==> x \\<in> A ==> y \\<in> A ==> (Abs x = Abs y) = (x = y)"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  assume x: "x \\<in> A" and y: "y \\<in> A"
-  show ?thesis
-  proof
-    assume "Abs x = Abs y"
-    hence "Rep (Abs x) = Rep (Abs y)" by simp
-    moreover from x have "Rep (Abs x) = x" by (rule Abs_inverse [OF tydef])
-    moreover from y have "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
-    ultimately show "x = y" by (simp only:)
-  next
-    assume "x = y"
-    thus "Abs x = Abs y" by simp
-  qed
-qed
-
-theorem Rep_cases:
-  "type_definition Rep Abs A ==> y \\<in> A ==> (!!x. y = Rep x ==> P) ==> P"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  assume y: "y \\<in> A" and r: "(!!x. y = Rep x ==> P)"
-  show P
-  proof (rule r)
-    from y have "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
-    thus "y = Rep (Abs y)" ..
-  qed
-qed
-
-theorem Abs_cases:
-  "type_definition Rep Abs A ==> (!!y. x = Abs y ==> y \\<in> A ==> P) ==> P"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  assume r: "!!y. x = Abs y ==> y \\<in> A ==> P"
-  show P
-  proof (rule r)
-    have "Abs (Rep x) = x" by (rule Rep_inverse [OF tydef])
-    thus "x = Abs (Rep x)" ..
-    show "Rep x \\<in> A" by (rule Rep [OF tydef])
-  qed
-qed
-
-theorem Rep_induct:
-  "type_definition Rep Abs A ==> y \\<in> A ==> (!!x. P (Rep x)) ==> P y"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  assume "!!x. P (Rep x)" hence "P (Rep (Abs y))" .
-  moreover assume "y \\<in> A" hence "Rep (Abs y) = y" by (rule Abs_inverse [OF tydef])
-  ultimately show "P y" by (simp only:)
-qed
-
-theorem Abs_induct:
-  "type_definition Rep Abs A ==> (!!y. y \\<in> A ==> P (Abs y)) ==> P x"
-proof -
-  assume tydef: "type_definition Rep Abs A"
-  assume r: "!!y. y \\<in> A ==> P (Abs y)"
-  have "Rep x \\<in> A" by (rule Rep [OF tydef])
-  hence "P (Abs (Rep x))" by (rule r)
-  moreover have "Abs (Rep x) = x" by (rule Rep_inverse [OF tydef])
-  ultimately show "P x" by (simp only:)
-qed
-
-setup InductAttrib.setup
-use "Tools/typedef_package.ML"
-
-end