author  lcp 
Tue, 05 Oct 1993 15:21:29 +0100  
changeset 25  3ac1c0c0016e 
parent 6  8ce8c4d13d4d 
child 124  858ab9a9b047 
permissions  rwrr 
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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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8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
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diff
changeset

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rec_def "rec(k,a,b) == transrec(k, %n f. nat_case(a, %m. b(m, f`m), n))" 
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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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3ac1c0c0016e
ordinal: DEFINITION of < and le to replace : and <= on ordinals! Many
lcp
parents:
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diff
changeset

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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

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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 