src/ZF/Ordinal.thy
changeset 69587 53982d5ec0bb
parent 61798 27f3c10b0b50
child 69593 3dda49e08b9d
equal deleted inserted replaced
69586:9171d1ce5a35 69587:53982d5ec0bb
    18 definition
    18 definition
    19   Ord  :: "i=>o"  where
    19   Ord  :: "i=>o"  where
    20     "Ord(i)      == Transset(i) & (\<forall>x\<in>i. Transset(x))"
    20     "Ord(i)      == Transset(i) & (\<forall>x\<in>i. Transset(x))"
    21 
    21 
    22 definition
    22 definition
    23   lt        :: "[i,i] => o"  (infixl "<" 50)   (*less-than on ordinals*)  where
    23   lt        :: "[i,i] => o"  (infixl \<open><\<close> 50)   (*less-than on ordinals*)  where
    24     "i<j         == i\<in>j & Ord(j)"
    24     "i<j         == i\<in>j & Ord(j)"
    25 
    25 
    26 definition
    26 definition
    27   Limit         :: "i=>o"  where
    27   Limit         :: "i=>o"  where
    28     "Limit(i)    == Ord(i) & 0<i & (\<forall>y. y<i \<longrightarrow> succ(y)<i)"
    28     "Limit(i)    == Ord(i) & 0<i & (\<forall>y. y<i \<longrightarrow> succ(y)<i)"
    29 
    29 
    30 abbreviation
    30 abbreviation
    31   le  (infixl "\<le>" 50) where
    31   le  (infixl \<open>\<le>\<close> 50) where
    32   "x \<le> y == x < succ(y)"
    32   "x \<le> y == x < succ(y)"
    33 
    33 
    34 
    34 
    35 subsection\<open>Rules for Transset\<close>
    35 subsection\<open>Rules for Transset\<close>
    36 
    36