ML's mathbox:
ML's mathbox:

- Add a definition for "Cartesian exponentiation", written
  ` ( U ^^ N ) ` where ` N ` is an ordinal natural number.
  See ~ finxp0 , ~ finxp1o , and ~ finxp2o for examples of its value,
  and ~ finxpsuc for its value at a successor.
- Add ~ csbopg2 . Compared to ~ csbopg , it has the disadvantage that
  its proof depends on the construction of ordered pairs, but in
  exchange it has no distinct variable conditions.
- Add multiple csb*g theorems.
- Add other miscellaneous theorems used in the proofs of the above.

The Cartesian exponentiation definition works on proper classes.
Compared to ~ df-ixp and ~ df-map , it has the disadvantage of being
limited to finite exponents, but its advantage is that it integrates
better with functions and relations, since it produces genuine nested
ordered pairs.

metamath/set.mm,metamath/set.mm,metamath/set.mm