| author | paulson |
| Tue, 18 Aug 1998 10:24:54 +0200 | |
| changeset 5330 | 8c9fadda81f4 |
| parent 5101 | 52e7c75acfe6 |
| child 5616 | 497eeeace3fc |
| permissions | -rw-r--r-- |
| 1475 | 1 |
(* Title: HOL/Finite.thy |
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ID: $Id$ |
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Author: Lawrence C Paulson & Tobias Nipkow |
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Copyright 1995 University of Cambridge & TU Muenchen |
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Finite sets and their cardinality |
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*) |
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Finite = Divides + Power + Inductive + |
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3413
c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
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consts Finites :: 'a set set |
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3413
c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
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inductive "Finites" |
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intrs |
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3413
c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
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emptyI "{} : Finites"
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c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
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insertI "A : Finites ==> insert a A : Finites" |
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c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
17 |
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c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
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syntax finite :: 'a set => bool |
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c1f63cc3a768
Finite.ML Finite.thy: Replaced `finite subset of' by mere `finite'.
nipkow
parents:
3389
diff
changeset
|
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translations "finite A" == "A : Finites" |
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constdefs |
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card :: 'a set => nat |
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"card A == LEAST n. ? f. A = {f i |i. i<n}"
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end |