src/ZF/Order.thy
 author paulson Thu Jul 11 15:28:10 1996 +0200 (1996-07-11) changeset 1851 7b1e1c298e50 parent 1478 2b8c2a7547ab child 2469 b50b8c0eec01 permissions -rw-r--r--
Corrected indentation
```     1 (*  Title:      ZF/Order.thy
```
```     2     ID:         \$Id\$
```
```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1994  University of Cambridge
```
```     5
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```     6 Orders in Zermelo-Fraenkel Set Theory
```
```     7 *)
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```     8
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```     9 Order = WF + Perm +
```
```    10 consts
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```    11   part_ord        :: [i,i]=>o           (*Strict partial ordering*)
```
```    12   linear, tot_ord :: [i,i]=>o           (*Strict total ordering*)
```
```    13   well_ord        :: [i,i]=>o           (*Well-ordering*)
```
```    14   mono_map        :: [i,i,i,i]=>i       (*Order-preserving maps*)
```
```    15   ord_iso         :: [i,i,i,i]=>i       (*Order isomorphisms*)
```
```    16   pred            :: [i,i,i]=>i		(*Set of predecessors*)
```
```    17   ord_iso_map     :: [i,i,i,i]=>i       (*Construction for linearity theorem*)
```
```    18
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```    19 defs
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```    20   part_ord_def "part_ord(A,r) == irrefl(A,r) & trans[A](r)"
```
```    21
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```    22   linear_def   "linear(A,r) == (ALL x:A. ALL y:A. <x,y>:r | x=y | <y,x>:r)"
```
```    23
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```    24   tot_ord_def  "tot_ord(A,r) == part_ord(A,r) & linear(A,r)"
```
```    25
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```    26   well_ord_def "well_ord(A,r) == tot_ord(A,r) & wf[A](r)"
```
```    27
```
```    28   mono_map_def "mono_map(A,r,B,s) ==
```
```    29                    {f: A->B. ALL x:A. ALL y:A. <x,y>:r --> <f`x,f`y>:s}"
```
```    30
```
```    31   ord_iso_def  "ord_iso(A,r,B,s) ==
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```    32                    {f: bij(A,B). ALL x:A. ALL y:A. <x,y>:r <-> <f`x,f`y>:s}"
```
```    33
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```    34   pred_def     "pred(A,x,r) == {y:A. <y,x>:r}"
```
```    35
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```    36   ord_iso_map_def
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```    37      "ord_iso_map(A,r,B,s) ==
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```    38        UN x:A. UN y:B. UN f: ord_iso(pred(A,x,r), r, pred(B,y,s), s).
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```    39             {<x,y>}"
```
```    40
```
```    41 end
```