equal
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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 |