src/HOL/Library/Ramsey.thy
changeset 34941 156925dd67af
parent 32960 69916a850301
child 35175 61255c81da01
     1.1 --- a/src/HOL/Library/Ramsey.thy	Sat Jan 16 17:15:27 2010 +0100
     1.2 +++ b/src/HOL/Library/Ramsey.thy	Sat Jan 16 17:15:28 2010 +0100
     1.3 @@ -12,13 +12,10 @@
     1.4  
     1.5  subsubsection {* ``Axiom'' of Dependent Choice *}
     1.6  
     1.7 -consts choice :: "('a => bool) => ('a * 'a) set => nat => 'a"
     1.8 +primrec choice :: "('a => bool) => ('a * 'a) set => nat => 'a" where
     1.9    --{*An integer-indexed chain of choices*}
    1.10 -primrec
    1.11 -  choice_0:   "choice P r 0 = (SOME x. P x)"
    1.12 -
    1.13 -  choice_Suc: "choice P r (Suc n) = (SOME y. P y & (choice P r n, y) \<in> r)"
    1.14 -
    1.15 +    choice_0:   "choice P r 0 = (SOME x. P x)"
    1.16 +  | choice_Suc: "choice P r (Suc n) = (SOME y. P y & (choice P r n, y) \<in> r)"
    1.17  
    1.18  lemma choice_n: 
    1.19    assumes P0: "P x0"