Lines Matching defs:standard
27 non-well-founded data structures within the standard {\sc zf} axioms including
451 defined in the standard way, $\pair{a,b}\equiv\{\{a\},\{a,b\}\}$. Recall
777 encodings of ordered pairs. The non-standard ordered pairs mentioned below
947 \tdx{eta} are the standard conversions. We essentially have a
1092 \caption{Non-standard pairs, products and sums} \label{zf-qpair}
1096 \subsection{Non-standard ordered pairs}
1103 versions for standard ordered pairs. The theory goes on to define a
1104 non-standard notion of disjoint sum using non-standard pairs. All of these
1105 concepts satisfy the same properties as their standard counterparts; in
1323 under the non-standard product and sum.
1820 induct \textrm{the standard induction rule}
2257 standard example: the accessible part of a relation. Note the use
2310 induct \textrm{the standard induction rule}