src/ZF/Arith.thy
author clasohm
Thu, 16 Sep 1993 12:20:38 +0200
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(*  Title: 	ZF/arith.thy
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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Arithmetic operators and their definitions
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*)
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Arith = Epsilon +
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consts
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    rec  :: "[i, i, [i,i]=>i]=>i"
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    "#*" :: "[i,i]=>i"      		(infixl 70)
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    div  :: "[i,i]=>i"      		(infixl 70) 
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    mod  :: "[i,i]=>i"      		(infixl 70)
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    "#+" :: "[i,i]=>i"      		(infixl 65)
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    "#-" :: "[i,i]=>i"      		(infixl 65)
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rules
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    rec_def  "rec(k,a,b) ==  transrec(k, %n f. nat_case(n, a, %m. b(m, f`m)))"
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    add_def  "m#+n == rec(m, n, %u v.succ(v))"
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    diff_def "m#-n == rec(n, m, %u v. rec(v, 0, %x y.x))"
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    mult_def "m#*n == rec(m, 0, %u v. n #+ v)"
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    mod_def  "m mod n == transrec(m, %j f. if(j:n, j, f`(j#-n)))"
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    div_def  "m div n == transrec(m, %j f. if(j:n, 0, succ(f`(j#-n))))"
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end