src/ZF/arith.thy
author paulson
Fri, 11 Aug 2000 13:26:40 +0200
changeset 9577 9e66e8ed8237
parent 124 858ab9a9b047
permissions -rw-r--r--
ZF arith
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     1
(*  Title: 	ZF/arith.thy
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     2
    ID:         $Id$
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     4
    Copyright   1992  University of Cambridge
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     5
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     6
Arithmetic operators and their definitions
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     7
*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     8
124
858ab9a9b047 made pseudo theories for all ML files;
clasohm
parents: 25
diff changeset
     9
Arith = Epsilon + "simpdata" +
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    10
consts
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    11
    rec  :: "[i, i, [i,i]=>i]=>i"
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    12
    "#*" :: "[i,i]=>i"      		(infixl 70)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    13
    div  :: "[i,i]=>i"      		(infixl 70) 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    14
    mod  :: "[i,i]=>i"      		(infixl 70)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    15
    "#+" :: "[i,i]=>i"      		(infixl 65)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    16
    "#-" :: "[i,i]=>i"      		(infixl 65)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    17
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    18
rules
6
8ce8c4d13d4d Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents: 0
diff changeset
    19
    rec_def  "rec(k,a,b) ==  transrec(k, %n f. nat_case(a, %m. b(m, f`m), n))"
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    20
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    21
    add_def  "m#+n == rec(m, n, %u v.succ(v))"
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    22
    diff_def "m#-n == rec(n, m, %u v. rec(v, 0, %x y.x))"
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    23
    mult_def "m#*n == rec(m, 0, %u v. n #+ v)"
25
3ac1c0c0016e ordinal: DEFINITION of < and le to replace : and <= on ordinals! Many
lcp
parents: 6
diff changeset
    24
    mod_def  "m mod n == transrec(m, %j f. if(j<n, j, f`(j#-n)))"
3ac1c0c0016e ordinal: DEFINITION of < and le to replace : and <= on ordinals! Many
lcp
parents: 6
diff changeset
    25
    div_def  "m div n == transrec(m, %j f. if(j<n, 0, succ(f`(j#-n))))"
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    26
end