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
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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
     5 
     6 Ramsey's Theorem (finite exponent 2 version)
     7 
     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
    13 
    14 See also
    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 *)
    20 
    21 Ramsey = Arith +
    22 consts
    23   Symmetric             :: i=>o
    24   Atleast               :: [i,i]=>o
    25   Clique,Indept,Ramsey  :: [i,i,i]=>o
    26 
    27 defs
    28 
    29   Symmetric_def
    30     "Symmetric(E) == (ALL x y. <x,y>:E --> <y,x>:E)"
    31 
    32   Clique_def
    33     "Clique(C,V,E) == (C<=V) & (ALL x:C. ALL y:C. x~=y --> <x,y> : E)"
    34 
    35   Indept_def
    36     "Indept(I,V,E) == (I<=V) & (ALL x:I. ALL y:I. x~=y --> <x,y> ~: E)"
    37 
    38   Atleast_def
    39     "Atleast(n,S) == (EX f. f: inj(n,S))"
    40 
    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))"
    45 
    46 end