| author | wenzelm |
| Mon, 18 May 1998 18:10:43 +0200 | |
| changeset 4941 | ac5da3e767b0 |
| parent 3840 | e0baea4d485a |
| child 6070 | 032babd0120b |
| permissions | -rw-r--r-- |
| 1478 | 1 |
(* 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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defs |
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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:
6
diff
changeset
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mod_def "m mod n == transrec(m, %j f. if(j<n, j, f`(j#-n)))" |
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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 |