src/ZF/ZF.thy
changeset 485 5e00a676a211
parent 351 1718ce07a584
child 516 1957113f0d7d
equal deleted inserted replaced
484:70b789956bd3 485:5e00a676a211
   131  (* ZF axioms -- see Suppes p.238
   131  (* ZF axioms -- see Suppes p.238
   132     Axioms for Union, Pow and Replace state existence only,
   132     Axioms for Union, Pow and Replace state existence only,
   133         uniqueness is derivable using extensionality.  *)
   133         uniqueness is derivable using extensionality.  *)
   134 
   134 
   135 extension       "A = B <-> A <= B & B <= A"
   135 extension       "A = B <-> A <= B & B <= A"
   136 union_iff       "A : Union(C) <-> (EX B:C. A:B)"
   136 Union_iff       "A : Union(C) <-> (EX B:C. A:B)"
   137 power_set       "A : Pow(B) <-> A <= B"
   137 Pow_iff         "A : Pow(B) <-> A <= B"
   138 succ_def        "succ(i) == cons(i,i)"
   138 succ_def        "succ(i) == cons(i,i)"
   139 
   139 
   140  (*We may name this set, though it is not uniquely defined. *)
   140  (*We may name this set, though it is not uniquely defined. *)
   141 infinity        "0:Inf & (ALL y:Inf. succ(y): Inf)"
   141 infinity        "0:Inf & (ALL y:Inf. succ(y): Inf)"
   142 
   142