src/CTT/Arith.thy

+(*  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