--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CTT/arith.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,24 @@
+(* Title: CTT/arith
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1991 University of Cambridge
+
+Arithmetic operators and their definitions
+
+Proves about elementary arithmetic: addition, multiplication, etc.
+Tests definitions and simplifier.
+*)
+
+Arith = CTT +
+
+consts "#+","-","|-|" :: "[i,i]=>i" (infixr 65)
+ "#*",div,mod :: "[i,i]=>i" (infixr 70)
+
+rules
+ add_def "a#+b == rec(a, b, %u v.succ(v))"
+ diff_def "a-b == rec(b, a, %u v.rec(v, 0, %x y.x))"
+ absdiff_def "a|-|b == (a-b) #+ (b-a)"
+ mult_def "a#*b == rec(a, 0, %u v. b #+ v)"
+ mod_def "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y.succ(v)))"
+ div_def "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y.v))"
+end