author  nipkow 
Fri, 24 Nov 2000 16:49:27 +0100  
changeset 10519  ade64af4c57c 
parent 9508  4d01dbf6ded7 
child 11049  7eef34adb852 
permissions  rwrr 
9508
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Chinese Remainder Theorem, Wilsons Theorem, etc., by T M Masmussen
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(* Title: BijectionRel.thy 
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Chinese Remainder Theorem, Wilsons Theorem, etc., by T M Masmussen
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ID: $Id$ 
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Chinese Remainder Theorem, Wilsons Theorem, etc., by T M Masmussen
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Author: Thomas M. Rasmussen 
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Copyright 2000 University of Cambridge 
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*) 
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BijectionRel = Main + 
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Chinese Remainder Theorem, Wilsons Theorem, etc., by T M Masmussen
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consts 
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bijR :: "(['a, 'b] => bool) => ('a set * 'b set) set" 
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inductive "bijR P" 
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intrs 
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empty "({},{}) : bijR P" 
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insert "[ P a b; a ~: A; b ~: B; (A,B) : bijR P ] \ 
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\ ==> (insert a A, insert b B) : bijR P" 
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(* Add extra condition to insert: ALL b:B. ~(P a b) (and similar for A) *) 
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consts 
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bijP :: "(['a, 'a] => bool) => 'a set => bool" 
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defs 
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bijP_def "bijP P F == (ALL a b. a:F & P a b > b:F)" 
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consts 
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uniqP :: "(['a, 'a] => bool) => bool" 
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symP :: "(['a, 'a] => bool) => bool" 
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defs 
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uniqP_def "uniqP P == (ALL a b c d. P a b & P c d > (a=c) = (b=d))" 
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symP_def "symP P == (ALL a b. (P a b) = (P b a))" 
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consts 
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bijER :: "(['a, 'a] => bool) => 'a set set" 
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inductive "bijER P" 
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intrs 
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empty "{} : bijER P" 
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insert1 "[ P a a; a ~: A; A : bijER P ] \ 
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\ ==> (insert a A) : bijER P" 
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insert2 "[ P a b; a ~= b; a ~: A; b ~: A; A : bijER P ] \ 
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\ ==> (insert a (insert b A)) : bijER P" 
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end 
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