src/ZF/ex/Ramsey.thy
 author clasohm Tue Feb 06 12:27:17 1996 +0100 (1996-02-06) changeset 1478 2b8c2a7547ab parent 1401 0c439768f45c child 11316 b4e71bd751e4 permissions -rw-r--r--
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1 (*  Title:      ZF/ex/ramsey.thy
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1992  University of Cambridge
6 Ramsey's Theorem (finite exponent 2 version)
8 Based upon the article
9     D Basin and M Kaufmann,
10     The Boyer-Moore Prover and Nuprl: An Experimental Comparison.
11     In G Huet and G Plotkin, editors, Logical Frameworks.
12     (CUP, 1991), pages 89--119
15     M Kaufmann,
16     An example in NQTHM: Ramsey's Theorem
17     Internal Note, Computational Logic, Inc., Austin, Texas 78703
18     Available from the author: kaufmann@cli.com
19 *)
21 Ramsey = Arith +
22 consts
23   Symmetric             :: i=>o
24   Atleast               :: [i,i]=>o
25   Clique,Indept,Ramsey  :: [i,i,i]=>o
27 defs
29   Symmetric_def
30     "Symmetric(E) == (ALL x y. <x,y>:E --> <y,x>:E)"
32   Clique_def
33     "Clique(C,V,E) == (C<=V) & (ALL x:C. ALL y:C. x~=y --> <x,y> : E)"
35   Indept_def
36     "Indept(I,V,E) == (I<=V) & (ALL x:I. ALL y:I. x~=y --> <x,y> ~: E)"
38   Atleast_def
39     "Atleast(n,S) == (EX f. f: inj(n,S))"
41   Ramsey_def
42     "Ramsey(n,i,j) == ALL V E. Symmetric(E) & Atleast(n,V) -->
43          (EX C. Clique(C,V,E) & Atleast(i,C)) |
44          (EX I. Indept(I,V,E) & Atleast(j,I))"
46 end