src/ZF/OrderArith.thy
 author lcp Tue Nov 29 00:31:31 1994 +0100 (1994-11-29 ago) changeset 753 ec86863e87c8 parent 437 435875e4b21d child 1155 928a16e02f9f permissions -rw-r--r--
replaced "rules" by "defs"
```     1 (*  Title: 	ZF/OrderArith.thy
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```     2     ID:         \$Id\$
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```     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1994  University of Cambridge
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```     5
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```     6 Towards ordinal arithmetic
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```     7 *)
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```     8
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```     9 OrderArith = Order + Sum +
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```    10 consts
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```    11   radd, rmult      :: "[i,i,i,i]=>i"
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```    12   rvimage          :: "[i,i,i]=>i"
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```    13
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```    14 defs
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```    15   (*disjoint sum of two relations; underlies ordinal addition*)
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```    16   radd_def "radd(A,r,B,s) == \
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```    17 \                {z: (A+B) * (A+B).  \
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```    18 \                    (EX x y. z = <Inl(x), Inr(y)>)   | 	 \
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```    19 \                    (EX x' x. z = <Inl(x'), Inl(x)> & <x',x>:r)   | 	 \
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```    20 \                    (EX y' y. z = <Inr(y'), Inr(y)> & <y',y>:s)}"
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```    21
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```    22   (*lexicographic product of two relations; underlies ordinal multiplication*)
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```    23   rmult_def "rmult(A,r,B,s) == \
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```    24 \                {z: (A*B) * (A*B).  \
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```    25 \                    EX x' y' x y. z = <<x',y'>, <x,y>> &	 \
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```    26 \                       (<x',x>: r | (x'=x & <y',y>: s))}"
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```    27
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```    28   (*inverse image of a relation*)
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```    29   rvimage_def "rvimage(A,f,r) == {z: A*A. EX x y. z = <x,y> & <f`x,f`y>: r}"
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```    30
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```    31 end
```