
diff -r 629f3a92863e -r 0ddd8028f98c src/FOL/ex/NatClass.thy
--- a/src/FOL/ex/NatClass.thy	Thu Feb 26 10:13:43 2009 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,90 +0,0 @@
-(*  Title:      FOL/ex/NatClass.thy
-    ID:         $Id$
-    Author:     Markus Wenzel, TU Muenchen
-*)
-
-theory NatClass
-imports FOL
-begin
-
-text {*
-  This is an abstract version of theory @{text "Nat"}. Instead of
-  axiomatizing a single type @{text nat} we define the class of all
-  these types (up to isomorphism).
-
-  Note: The @{text rec} operator had to be made \emph{monomorphic},
-  because class axioms may not contain more than one type variable.
-*}
-
-consts
-  0 :: 'a    ("0")
-  Suc :: "'a => 'a"
-  rec :: "['a, 'a, ['a, 'a] => 'a] => 'a"
-
-axclass
-  nat < "term"
-  induct:        "[| P(0); !!x. P(x) ==> P(Suc(x)) |] ==> P(n)"
-  Suc_inject:    "Suc(m) = Suc(n) ==> m = n"
-  Suc_neq_0:     "Suc(m) = 0 ==> R"
-  rec_0:         "rec(0, a, f) = a"
-  rec_Suc:       "rec(Suc(m), a, f) = f(m, rec(m, a, f))"
-
-definition
-  add :: "['a::nat, 'a] => 'a"  (infixl "+" 60) where
-  "m + n = rec(m, n, %x y. Suc(y))"
-
-lemma Suc_n_not_n: "Suc(k) ~= (k::'a::nat)"
-apply (rule_tac n = k in induct)
-apply (rule notI)
-apply (erule Suc_neq_0)
-apply (rule notI)
-apply (erule notE)
-apply (erule Suc_inject)
-done
-
-lemma "(k+m)+n = k+(m+n)"
-apply (rule induct)
-back
-back
-back
-back
-back
-back
-oops
-
-lemma add_0 [simp]: "0+n = n"
-apply (unfold add_def)
-apply (rule rec_0)
-done
-
-lemma add_Suc [simp]: "Suc(m)+n = Suc(m+n)"
-apply (unfold add_def)
-apply (rule rec_Suc)
-done
-
-lemma add_assoc: "(k+m)+n = k+(m+n)"
-apply (rule_tac n = k in induct)
-apply simp
-apply simp
-done
-
-lemma add_0_right: "m+0 = m"
-apply (rule_tac n = m in induct)
-apply simp
-apply simp
-done
-
-lemma add_Suc_right: "m+Suc(n) = Suc(m+n)"
-apply (rule_tac n = m in induct)
-apply simp_all
-done
-
-lemma
-  assumes prem: "!!n. f(Suc(n)) = Suc(f(n))"
-  shows "f(i+j) = i+f(j)"
-apply (rule_tac n = i in induct)
-apply simp
-apply (simp add: prem)
-done
-
-end




