--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/nat.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,26 @@
+(* Title: FOL/ex/nat.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1992 University of Cambridge
+
+Examples for the manual "Introduction to Isabelle"
+
+Theory of the natural numbers: Peano's axioms, primitive recursion
+
+INCOMPATIBLE with nat2.thy, Nipkow's example
+*)
+
+Nat = FOL +
+types nat 0
+arities nat :: term
+consts "0" :: "nat" ("0")
+ Suc :: "nat=>nat"
+ rec :: "[nat, 'a, [nat,'a]=>'a] => 'a"
+ "+" :: "[nat, nat] => nat" (infixl 60)
+rules 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))"
+ add_def "m+n == rec(m, n, %x y. Suc(y))"
+end