
diff -r a935175fe6b6 -r f462e49eaf11 src/HOL/ex/Quickcheck_Lattice_Examples.thy
--- a/src/HOL/ex/Quickcheck_Lattice_Examples.thy	Tue Feb 21 23:25:36 2012 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,141 +0,0 @@
-(*  Title:      HOL/ex/Quickcheck_Lattice_Examples.thy
-    Author:     Lukas Bulwahn
-    Copyright   2010 TU Muenchen
-*)
-
-theory Quickcheck_Lattice_Examples
-imports "~~/src/HOL/Library/Quickcheck_Types"
-begin
-
-text {* We show how other default types help to find counterexamples to propositions if
-  the standard default type @{typ int} is insufficient. *}
-
-notation
-  less_eq  (infix "\<sqsubseteq>" 50) and
-  less  (infix "\<sqsubset>" 50) and
-  top ("\<top>") and
-  bot ("\<bottom>") and
-  inf (infixl "\<sqinter>" 70) and
-  sup (infixl "\<squnion>" 65)
-
-declare [[quickcheck_narrowing_active = false, quickcheck_timeout = 3600]]
-
-subsection {* Distributive lattices *}
-
-lemma sup_inf_distrib2:
- "((y :: 'a :: distrib_lattice) \<sqinter> z) \<squnion> x = (y \<squnion> x) \<sqinter> (z \<squnion> x)"
-  quickcheck[expect = no_counterexample]
-by(simp add: inf_sup_aci sup_inf_distrib1)
-
-lemma sup_inf_distrib2_1:
- "((y :: 'a :: lattice) \<sqinter> z) \<squnion> x = (y \<squnion> x) \<sqinter> (z \<squnion> x)"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma sup_inf_distrib2_2:
- "((y :: 'a :: distrib_lattice) \<sqinter> z') \<squnion> x = (y \<squnion> x) \<sqinter> (z \<squnion> x)"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_sup_distrib1_1:
- "(x :: 'a :: distrib_lattice) \<sqinter> (y \<squnion> z) = (x \<sqinter> y) \<squnion> (x' \<sqinter> z)"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_sup_distrib2_1:
- "((y :: 'a :: distrib_lattice) \<squnion> z) \<sqinter> x = (y \<sqinter> x) \<squnion> (y \<sqinter> x)"
-  quickcheck[expect = counterexample]
-  oops
-
-subsection {* Bounded lattices *}
-
-lemma inf_bot_left [simp]:
-  "\<bottom> \<sqinter> (x :: 'a :: bounded_lattice_bot) = \<bottom>"
-  quickcheck[expect = no_counterexample]
-  by (rule inf_absorb1) simp
-
-lemma inf_bot_left_1:
-  "\<bottom> \<sqinter> (x :: 'a :: bounded_lattice_bot) = x"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_bot_left_2:
-  "y \<sqinter> (x :: 'a :: bounded_lattice_bot) = \<bottom>"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_bot_left_3:
-  "x \<noteq> \<bottom> ==> y \<sqinter> (x :: 'a :: bounded_lattice_bot) \<noteq> \<bottom>"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_bot_right [simp]:
-  "(x :: 'a :: bounded_lattice_bot) \<sqinter> \<bottom> = \<bottom>"
-  quickcheck[expect = no_counterexample]
-  by (rule inf_absorb2) simp
-
-lemma inf_bot_right_1:
-  "x \<noteq> \<bottom> ==> (x :: 'a :: bounded_lattice_bot) \<sqinter> \<bottom> = y"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_bot_right_2:
-  "(x :: 'a :: bounded_lattice_bot) \<sqinter> \<bottom> ~= \<bottom>"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma inf_bot_right [simp]:
-  "(x :: 'a :: bounded_lattice_bot) \<squnion> \<bottom> = \<bottom>"
-  quickcheck[expect = counterexample]
-  oops
-
-lemma sup_bot_left [simp]:
-  "\<bottom> \<squnion> (x :: 'a :: bounded_lattice_bot) = x"
-  quickcheck[expect = no_counterexample]
-  by (rule sup_absorb2) simp
-
-lemma sup_bot_right [simp]:
-  "(x :: 'a :: bounded_lattice_bot) \<squnion> \<bottom> = x"
-  quickcheck[expect = no_counterexample]
-  by (rule sup_absorb1) simp
-
-lemma sup_eq_bot_iff [simp]:
-  "(x :: 'a :: bounded_lattice_bot) \<squnion> y = \<bottom> \<longleftrightarrow> x = \<bottom> \<and> y = \<bottom>"
-  quickcheck[expect = no_counterexample]
-  by (simp add: eq_iff)
-
-lemma sup_top_left [simp]:
-  "\<top> \<squnion> (x :: 'a :: bounded_lattice_top) = \<top>"
-  quickcheck[expect = no_counterexample]
-  by (rule sup_absorb1) simp
-
-lemma sup_top_right [simp]:
-  "(x :: 'a :: bounded_lattice_top) \<squnion> \<top> = \<top>"
-  quickcheck[expect = no_counterexample]
-  by (rule sup_absorb2) simp
-
-lemma inf_top_left [simp]:
-  "\<top> \<sqinter> x = (x :: 'a :: bounded_lattice_top)"
-  quickcheck[expect = no_counterexample]
-  by (rule inf_absorb2) simp
-
-lemma inf_top_right [simp]:
-  "x \<sqinter> \<top> = (x :: 'a :: bounded_lattice_top)"
-  quickcheck[expect = no_counterexample]
-  by (rule inf_absorb1) simp
-
-lemma inf_eq_top_iff [simp]:
-  "(x :: 'a :: bounded_lattice_top) \<sqinter> y = \<top> \<longleftrightarrow> x = \<top> \<and> y = \<top>"
-  quickcheck[expect = no_counterexample]
-  by (simp add: eq_iff)
-
-
-no_notation
-  less_eq  (infix "\<sqsubseteq>" 50) and
-  less (infix "\<sqsubset>" 50) and
-  inf  (infixl "\<sqinter>" 70) and
-  sup  (infixl "\<squnion>" 65) and
-  top ("\<top>") and
-  bot ("\<bottom>")
-
-end




