# HG changeset patch
# User wenzelm
# Date 1003082531 -7200
# Node ID 89cff5bfe3b164591d1feed6e0b74bb07cdedebe
# Parent  3e400964893e3e030f9e9cb0ea5cb8e4ae01087b
removed Ord.thy (now part of HOL.thy).

diff -r 3e400964893e -r 89cff5bfe3b1 src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Sun Oct 14 20:01:42 2001 +0200
+++ b/src/HOL/IsaMakefile	Sun Oct 14 20:02:11 2001 +0200
@@ -91,7 +91,7 @@
   Inverse_Image.ML Inverse_Image.thy Lfp.ML \
   Lfp.thy List.ML List.thy Main.ML Main.thy Map.ML Map.thy Nat.ML \
   Nat.thy NatArith.ML NatArith.thy NatDef.ML NatDef.thy Numeral.thy \
-  Option.ML Option.thy Ord.thy Power.ML Power.thy PreList.thy \
+  Option.ML Option.thy Power.ML Power.thy PreList.thy \
   Product_Type_lemmas.ML Product_Type.thy ROOT.ML Recdef.thy Record.thy \
   Relation.ML Relation.thy Relation_Power.ML Relation_Power.thy \
   SVC_Oracle.ML SVC_Oracle.thy Set.ML Set.thy SetInterval.ML \
diff -r 3e400964893e -r 89cff5bfe3b1 src/HOL/Ord.thy
--- a/src/HOL/Ord.thy	Sun Oct 14 20:01:42 2001 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,399 +0,0 @@
-(*  Title:      HOL/Ord.thy
-    ID:         $Id$
-    Author:     Tobias Nipkow, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
-
-Type classes for order signatures and orders.
-*)
-
-theory Ord = HOL:
-
-
-axclass
-  ord < "term"
-
-syntax
-  "op <"        :: "['a::ord, 'a] => bool"             ("op <")
-  "op <="       :: "['a::ord, 'a] => bool"             ("op <=")
-
-global
-
-consts
-  "op <"        :: "['a::ord, 'a] => bool"             ("(_/ < _)"  [50, 51] 50)
-  "op <="       :: "['a::ord, 'a] => bool"             ("(_/ <= _)" [50, 51] 50)
-
-local
-
-syntax (symbols)
-  "op <="       :: "['a::ord, 'a] => bool"             ("op \\<le>")
-  "op <="       :: "['a::ord, 'a] => bool"             ("(_/ \\<le> _)"  [50, 51] 50)
-
-(*Tell Blast_tac about overloading of < and <= to reduce the risk of
-  its applying a rule for the wrong type*)
-ML {*
-Blast.overloaded ("op <" , domain_type);
-Blast.overloaded ("op <=", domain_type);
-*}
-
-
-constdefs
-  mono          :: "['a::ord => 'b::ord] => bool"      (*monotonicity*)
-                "mono(f)   == (!A B. A <= B --> f(A) <= f(B))"
-
-lemma monoI [intro?]: "[| !!A B. A <= B ==> f(A) <= f(B) |] ==> mono(f)"
-apply (unfold mono_def)
-apply fast
-done
-
-lemma monoD [dest?]: "[| mono(f);  A <= B |] ==> f(A) <= f(B)"
-apply (unfold mono_def)
-apply fast
-done
-
-
-constdefs
-  min     :: "['a::ord, 'a] => 'a"
-             "min a b   == (if a <= b then a else b)"
-  max     :: "['a::ord, 'a] => 'a"
-             "max a b   == (if a <= b then b else a)"
-
-lemma min_leastL: "(!!x. least <= x) ==> min least x = least"
-apply (simp add: min_def)
-done
-
-lemma min_of_mono: 
-  "!x y. (f x <= f y) = (x <= y) ==> min (f m) (f n) = f (min m n)"
-apply (simp add: min_def)
-done
-
-lemma max_leastL: "(!!x. least <= x) ==> max least x = x"
-apply (simp add: max_def)
-done
-
-lemma max_of_mono: 
-  "!x y. (f x <= f y) = (x <= y) ==> max (f m) (f n) = f (max m n)"
-apply (simp add: max_def)
-done
-
-
-section "Orders"
-
-axclass order < ord
-  order_refl [iff]:                          "x <= x"
-  order_trans:      "[| x <= y; y <= z |] ==> x <= z"
-  order_antisym:    "[| x <= y; y <= x |] ==> x = y"
-  order_less_le:    "(x < y) = (x <= y & x ~= y)"
-
-(** Reflexivity **)
-
-(*This form is useful with the classical reasoner*)
-lemma order_eq_refl: "!!x::'a::order. x = y ==> x <= y"
-apply (erule ssubst)
-apply (rule order_refl)
-done
-
-lemma order_less_irrefl [simp]: "~ x < (x::'a::order)"
-apply (simp (no_asm) add: order_less_le)
-done
-
-lemma order_le_less: "((x::'a::order) <= y) = (x < y | x = y)"
-apply (simp (no_asm) add: order_less_le)
-   (*NOT suitable for AddIffs, since it can cause PROOF FAILED*)
-apply (blast intro!: order_refl)
-done
-
-lemmas order_le_imp_less_or_eq = order_le_less [THEN iffD1, standard]
-
-lemma order_less_imp_le: "!!x::'a::order. x < y ==> x <= y"
-apply (simp add: order_less_le)
-done
-
-(** Asymmetry **)
-
-lemma order_less_not_sym: "(x::'a::order) < y ==> ~ (y<x)"
-apply (simp add: order_less_le order_antisym)
-done
-
-(* [| n<m;  ~P ==> m<n |] ==> P *)
-lemmas order_less_asym = order_less_not_sym [THEN contrapos_np, standard]
-
-(* Transitivity *)
-
-lemma order_less_trans: "!!x::'a::order. [| x < y; y < z |] ==> x < z"
-apply (simp add: order_less_le)
-apply (blast intro: order_trans order_antisym)
-done
-
-lemma order_le_less_trans: "!!x::'a::order. [| x <= y; y < z |] ==> x < z"
-apply (simp add: order_less_le)
-apply (blast intro: order_trans order_antisym)
-done
-
-lemma order_less_le_trans: "!!x::'a::order. [| x < y; y <= z |] ==> x < z"
-apply (simp add: order_less_le)
-apply (blast intro: order_trans order_antisym)
-done
-
-
-(** Useful for simplification, but too risky to include by default. **)
-
-lemma order_less_imp_not_less: "(x::'a::order) < y ==>  (~ y < x) = True"
-apply (blast elim: order_less_asym)
-done
-
-lemma order_less_imp_triv: "(x::'a::order) < y ==>  (y < x --> P) = True"
-apply (blast elim: order_less_asym)
-done
-
-lemma order_less_imp_not_eq: "(x::'a::order) < y ==>  (x = y) = False"
-apply auto
-done
-
-lemma order_less_imp_not_eq2: "(x::'a::order) < y ==>  (y = x) = False"
-apply auto
-done
-
-(* Other operators *)
-
-lemma min_leastR: "(!!x::'a::order. least <= x) ==> min x least = least"
-apply (simp (no_asm_simp) add: min_def)
-apply (blast intro: order_antisym)
-done
-
-lemma max_leastR: "(!!x::'a::order. least <= x) ==> max x least = x"
-apply (simp add: max_def)
-apply (blast intro: order_antisym)
-done
-
-
-(** Least value operator **)
-
-(*We can no longer use LeastM because the latter requires Hilbert-AC*)
-constdefs
-  Least    :: "('a::ord => bool) => 'a"               (binder "LEAST " 10)
-    "Least P == THE x. P x & (ALL y. P y --> x <= y)"
-
-lemma LeastI2:
-  "[| P (x::'a::order); 
-      !!y. P y ==> x <= y;
-      !!x. [| P x; \\<forall>y. P y --> x \\<le> y |] ==> Q x |]
-   ==> Q (Least P)";
-apply (unfold Least_def)
-apply (rule theI2)
-  apply (blast intro: order_antisym)+
-done
-
-lemma Least_equality:
-  "[| P (k::'a::order); !!x. P x ==> k <= x |] ==> (LEAST x. P x) = k";
-apply (simp add: Least_def)
-apply (rule the_equality)
-apply (auto intro!: order_antisym) 
-done
-
-section "Linear/Total Orders"
-
-axclass linorder < order
-  linorder_linear: "x <= y | y <= x"
-
-lemma linorder_less_linear: "!!x::'a::linorder. x<y | x=y | y<x"
-apply (simp (no_asm) add: order_less_le)
-apply (cut_tac linorder_linear)
-apply blast
-done
-
-lemma linorder_cases [case_names less equal greater]:
-  "[| (x::'a::linorder)<y ==> P; x=y ==> P; y<x ==> P |] ==> P"
-apply (cut_tac linorder_less_linear)
-apply blast
-done
-
-lemma linorder_not_less: "!!x::'a::linorder. (~ x < y) = (y <= x)"
-apply (simp (no_asm) add: order_less_le)
-apply (cut_tac linorder_linear)
-apply (blast intro: order_antisym)
-done
-
-lemma linorder_not_le: "!!x::'a::linorder. (~ x <= y) = (y < x)"
-apply (simp (no_asm) add: order_less_le)
-apply (cut_tac linorder_linear)
-apply (blast intro: order_antisym)
-done
-
-lemma linorder_neq_iff: "!!x::'a::linorder. (x ~= y) = (x<y | y<x)"
-apply (cut_tac x = "x" and y = "y" in linorder_less_linear)
-apply auto
-done
-
-(* eliminates ~= in premises *)
-lemmas linorder_neqE = linorder_neq_iff [THEN iffD1, THEN disjE, standard]
-
-section "min & max on (linear) orders"
-
-lemma min_same [simp]: "min (x::'a::order) x = x"
-apply (simp add: min_def)
-done
-
-lemma max_same [simp]: "max (x::'a::order) x = x"
-apply (simp add: max_def)
-done
-
-lemma le_max_iff_disj: "!!z::'a::linorder. (z <= max x y) = (z <= x | z <= y)"
-apply (unfold max_def)
-apply (simp (no_asm))
-apply (cut_tac linorder_linear)
-apply (blast intro: order_trans)
-done
-
-lemma le_maxI1: "(x::'a::linorder) <= max x y"
-apply (simp (no_asm) add: le_max_iff_disj)
-done
-
-lemma le_maxI2: "(y::'a::linorder) <= max x y"
-apply (simp (no_asm) add: le_max_iff_disj)
-done
-(*CANNOT use with AddSIs because blast_tac will give PROOF FAILED.*)
-
-lemma less_max_iff_disj: "!!z::'a::linorder. (z < max x y) = (z < x | z < y)"
-apply (simp (no_asm) add: max_def order_le_less)
-apply (cut_tac linorder_less_linear)
-apply (blast intro: order_less_trans)
-done
-
-lemma max_le_iff_conj [simp]: 
-  "!!z::'a::linorder. (max x y <= z) = (x <= z & y <= z)"
-apply (simp (no_asm) add: max_def)
-apply (cut_tac linorder_linear)
-apply (blast intro: order_trans)
-done
-
-lemma max_less_iff_conj [simp]: 
-  "!!z::'a::linorder. (max x y < z) = (x < z & y < z)"
-apply (simp (no_asm) add: order_le_less max_def)
-apply (cut_tac linorder_less_linear)
-apply (blast intro: order_less_trans)
-done
-
-lemma le_min_iff_conj [simp]: 
-  "!!z::'a::linorder. (z <= min x y) = (z <= x & z <= y)"
-apply (simp (no_asm) add: min_def)
-apply (cut_tac linorder_linear)
-apply (blast intro: order_trans)
-done
-(* AddIffs screws up a blast_tac in MiniML *)
-
-lemma min_less_iff_conj [simp]:
-  "!!z::'a::linorder. (z < min x y) = (z < x & z < y)"
-apply (simp (no_asm) add: order_le_less min_def)
-apply (cut_tac linorder_less_linear)
-apply (blast intro: order_less_trans)
-done
-
-lemma min_le_iff_disj: "!!z::'a::linorder. (min x y <= z) = (x <= z | y <= z)"
-apply (unfold min_def)
-apply (simp (no_asm))
-apply (cut_tac linorder_linear)
-apply (blast intro: order_trans)
-done
-
-lemma min_less_iff_disj: "!!z::'a::linorder. (min x y < z) = (x < z | y < z)"
-apply (unfold min_def)
-apply (simp (no_asm) add: order_le_less)
-apply (cut_tac linorder_less_linear)
-apply (blast intro: order_less_trans)
-done
-
-lemma split_min: 
- "P(min (i::'a::linorder) j) = ((i <= j --> P(i)) & (~ i <= j --> P(j)))"
-apply (simp (no_asm) add: min_def)
-done
-
-lemma split_max: 
- "P(max (i::'a::linorder) j) = ((i <= j --> P(j)) & (~ i <= j --> P(i)))"
-apply (simp (no_asm) add: max_def)
-done
-
-
-section "bounded quantifiers"
-
-syntax
-  "_lessAll" :: "[idt, 'a, bool] => bool"  ("(3ALL _<_./ _)"  [0, 0, 10] 10)
-  "_lessEx"  :: "[idt, 'a, bool] => bool"  ("(3EX _<_./ _)"  [0, 0, 10] 10)
-  "_leAll"   :: "[idt, 'a, bool] => bool"  ("(3ALL _<=_./ _)" [0, 0, 10] 10)
-  "_leEx"    :: "[idt, 'a, bool] => bool"  ("(3EX _<=_./ _)" [0, 0, 10] 10)
-
-syntax (symbols)
-  "_lessAll" :: "[idt, 'a, bool] => bool"  ("(3\\<forall>_<_./ _)"  [0, 0, 10] 10)
-  "_lessEx"  :: "[idt, 'a, bool] => bool"  ("(3\\<exists>_<_./ _)"  [0, 0, 10] 10)
-  "_leAll"   :: "[idt, 'a, bool] => bool"  ("(3\\<forall>_\\<le>_./ _)" [0, 0, 10] 10)
-  "_leEx"    :: "[idt, 'a, bool] => bool"  ("(3\\<exists>_\\<le>_./ _)" [0, 0, 10] 10)
-
-syntax (HOL)
-  "_lessAll" :: "[idt, 'a, bool] => bool"  ("(3! _<_./ _)"  [0, 0, 10] 10)
-  "_lessEx"  :: "[idt, 'a, bool] => bool"  ("(3? _<_./ _)"  [0, 0, 10] 10)
-  "_leAll"   :: "[idt, 'a, bool] => bool"  ("(3! _<=_./ _)" [0, 0, 10] 10)
-  "_leEx"    :: "[idt, 'a, bool] => bool"  ("(3? _<=_./ _)" [0, 0, 10] 10)
-
-translations
- "ALL x<y. P"   =>  "ALL x. x < y --> P"
- "EX x<y. P"    =>  "EX x. x < y  & P"
- "ALL x<=y. P"  =>  "ALL x. x <= y --> P"
- "EX x<=y. P"   =>  "EX x. x <= y & P"
-
-
-ML
-{*
-val Least_def = thm "Least_def";
-val Least_equality = thm "Least_equality";
-val mono_def = thm "mono_def";
-val monoI = thm "monoI";
-val monoD = thm "monoD";
-val min_def = thm "min_def";
-val min_of_mono = thm "min_of_mono";
-val max_def = thm "max_def";
-val max_of_mono = thm "max_of_mono";
-val min_leastL = thm "min_leastL";
-val max_leastL = thm "max_leastL";
-val min_leastR = thm "min_leastR";
-val max_leastR = thm "max_leastR";
-val order_eq_refl = thm "order_eq_refl";
-val order_less_irrefl = thm "order_less_irrefl";
-val order_le_less = thm "order_le_less";
-val order_le_imp_less_or_eq = thm "order_le_imp_less_or_eq";
-val order_less_imp_le = thm "order_less_imp_le";
-val order_less_not_sym = thm "order_less_not_sym";
-val order_less_asym = thm "order_less_asym";
-val order_less_trans = thm "order_less_trans";
-val order_le_less_trans = thm "order_le_less_trans";
-val order_less_le_trans = thm "order_less_le_trans";
-val order_less_imp_not_less = thm "order_less_imp_not_less";
-val order_less_imp_triv = thm "order_less_imp_triv";
-val order_less_imp_not_eq = thm "order_less_imp_not_eq";
-val order_less_imp_not_eq2 = thm "order_less_imp_not_eq2";
-val linorder_less_linear = thm "linorder_less_linear";
-val linorder_cases = thm "linorder_cases";
-val linorder_not_less = thm "linorder_not_less";
-val linorder_not_le = thm "linorder_not_le";
-val linorder_neq_iff = thm "linorder_neq_iff";
-val linorder_neqE = thm "linorder_neqE";
-val min_same = thm "min_same";
-val max_same = thm "max_same";
-val le_max_iff_disj = thm "le_max_iff_disj";
-val le_maxI1 = thm "le_maxI1";
-val le_maxI2 = thm "le_maxI2";
-val less_max_iff_disj = thm "less_max_iff_disj";
-val max_le_iff_conj = thm "max_le_iff_conj";
-val max_less_iff_conj = thm "max_less_iff_conj";
-val le_min_iff_conj = thm "le_min_iff_conj";
-val min_less_iff_conj = thm "min_less_iff_conj";
-val min_le_iff_disj = thm "min_le_iff_disj";
-val min_less_iff_disj = thm "min_less_iff_disj";
-val split_min = thm "split_min";
-val split_max = thm "split_max";
-val order_refl = thm "order_refl";
-val order_trans = thm "order_trans";
-val order_antisym = thm "order_antisym";
-val order_less_le = thm "order_less_le";
-val linorder_linear = thm "linorder_linear";
-*}
-
-end