
diff -r c2a4dccf6e67 -r ed576de7bddc src/HOL/AxClasses/Tutorial/Group.thy
--- a/src/HOL/AxClasses/Tutorial/Group.thy	Tue Oct 03 18:34:20 2000 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,129 +0,0 @@
-(*  Title:      HOL/AxClasses/Tutorial/Group.thy
-    ID:         $Id$
-    Author:     Markus Wenzel, TU Muenchen
-*)
-
-theory Group = Main:
-
-subsection {* Monoids and Groups *}
-
-consts
-  times :: "'a => 'a => 'a"    (infixl "[*]" 70)
-  inverse :: "'a => 'a"
-  one :: 'a
-
-
-axclass
-  monoid < "term"
-  assoc:      "(x [*] y) [*] z = x [*] (y [*] z)"
-  left_unit:  "one [*] x = x"
-  right_unit: "x [*] one = x"
-
-
-axclass
-  semigroup < "term"
-  assoc: "(x [*] y) [*] z = x [*] (y [*] z)"
-
-axclass
-  group < semigroup
-  left_unit:    "one [*] x = x"
-  left_inverse: "inverse x [*] x = one"
-
-axclass
-  agroup < group
-  commute: "x [*] y = y [*] x"
-
-
-subsection {* Abstract reasoning *}
-
-theorem group_right_inverse: "x [*] inverse x = (one::'a::group)"
-proof -
-  have "x [*] inverse x = one [*] (x [*] inverse x)"
-    by (simp only: group.left_unit)
-  also have "... = one [*] x [*] inverse x"
-    by (simp only: semigroup.assoc)
-  also have "... = inverse (inverse x) [*] inverse x [*] x [*] inverse x"
-    by (simp only: group.left_inverse)
-  also have "... = inverse (inverse x) [*] (inverse x [*] x) [*] inverse x"
-    by (simp only: semigroup.assoc)
-  also have "... = inverse (inverse x) [*] one [*] inverse x"
-    by (simp only: group.left_inverse)
-  also have "... = inverse (inverse x) [*] (one [*] inverse x)"
-    by (simp only: semigroup.assoc)
-  also have "... = inverse (inverse x) [*] inverse x"
-    by (simp only: group.left_unit)
-  also have "... = one"
-    by (simp only: group.left_inverse)
-  finally show ?thesis .
-qed
-
-theorem group_right_unit: "x [*] one = (x::'a::group)"
-proof -
-  have "x [*] one = x [*] (inverse x [*] x)"
-    by (simp only: group.left_inverse)
-  also have "... = x [*] inverse x [*] x"
-    by (simp only: semigroup.assoc)
-  also have "... = one [*] x"
-    by (simp only: group_right_inverse)
-  also have "... = x"
-    by (simp only: group.left_unit)
-  finally show ?thesis .
-qed
-
-
-subsection {* Abstract instantiation *}
-
-instance monoid < semigroup
-proof intro_classes
-  fix x y z :: "'a::monoid"
-  show "x [*] y [*] z = x [*] (y [*] z)"
-    by (rule monoid.assoc)
-qed
-
-instance group < monoid
-proof intro_classes
-  fix x y z :: "'a::group"
-  show "x [*] y [*] z = x [*] (y [*] z)"
-    by (rule semigroup.assoc)
-  show "one [*] x = x"
-    by (rule group.left_unit)
-  show "x [*] one = x"
-    by (rule group_right_unit)
-qed
-
-
-subsection {* Concrete instantiation *}
-
-defs (overloaded)
-  times_bool_def:   "x [*] y == x ~= (y::bool)"
-  inverse_bool_def: "inverse x == x::bool"
-  unit_bool_def:    "one == False"
-
-instance bool :: agroup
-proof (intro_classes,
-    unfold times_bool_def inverse_bool_def unit_bool_def)
-  fix x y z
-  show "((x ~= y) ~= z) = (x ~= (y ~= z))" by blast
-  show "(False ~= x) = x" by blast
-  show "(x ~= x) = False" by blast
-  show "(x ~= y) = (y ~= x)" by blast
-qed
-
-
-subsection {* Lifting and Functors *}
-
-defs (overloaded)
-  times_prod_def: "p [*] q == (fst p [*] fst q, snd p [*] snd q)"
-
-instance * :: (semigroup, semigroup) semigroup
-proof (intro_classes, unfold times_prod_def)
-  fix p q r :: "'a::semigroup * 'b::semigroup"
-  show
-    "(fst (fst p [*] fst q, snd p [*] snd q) [*] fst r,
-      snd (fst p [*] fst q, snd p [*] snd q) [*] snd r) =
-       (fst p [*] fst (fst q [*] fst r, snd q [*] snd r),
-        snd p [*] snd (fst q [*] fst r, snd q [*] snd r))"
-    by (simp add: semigroup.assoc)
-qed
-
-end




