src/ZF/wf.thy
 author clasohm Thu Sep 16 12:20:38 1993 +0200 (1993-09-16) changeset 0 a5a9c433f639 child 124 858ab9a9b047 permissions -rw-r--r--
Initial revision
```     1 (*  Title: 	ZF/wf.thy
```
```     2     ID:         \$Id\$
```
```     3     Author: 	Tobias Nipkow and Lawrence C Paulson
```
```     4     Copyright   1992  University of Cambridge
```
```     5
```
```     6 Well-founded Recursion
```
```     7 *)
```
```     8
```
```     9 WF = Trancl +
```
```    10 consts
```
```    11     wf		 ::      "i=>o"
```
```    12     wftrec,wfrec ::      "[i, i, [i,i]=>i] =>i"
```
```    13     is_recfun    ::      "[i, i, [i,i]=>i, i] =>o"
```
```    14     the_recfun   ::      "[i, i, [i,i]=>i] =>i"
```
```    15
```
```    16 rules
```
```    17   (*r is a well-founded relation*)
```
```    18   wf_def	 "wf(r) == ALL Z. Z=0 | (EX x:Z. ALL y. <y,x>:r --> ~ y:Z)"
```
```    19
```
```    20   is_recfun_def  "is_recfun(r,a,H,f) == \
```
```    21 \   			(f = (lam x: r-``{a}. H(x, restrict(f, r-``{x}))))"
```
```    22
```
```    23   the_recfun_def "the_recfun(r,a,H) == (THE f.is_recfun(r,a,H,f))"
```
```    24
```
```    25   wftrec_def  	 "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
```
```    26
```
```    27   (*public version.  Does not require r to be transitive*)
```
```    28   wfrec_def "wfrec(r,a,H) == wftrec(r^+, a, %x f. H(x, restrict(f,r-``{x})))"
```
```    29
```
```    30 end
```