\label{theorems}

The sections that follow list all theorems in the \ml{reals} library,
including definitions. The theorems are grouped into their theories, which
corresponds quite closely to a natural logical partitioning. When the
\ml{reals} library is loaded, only theorems in {\tt REAL} and {\tt TRANSC} are
set up to autoload (and not all of them). These should be all the theorems
needed for day-to-day use of the library. Other definitions and theorems may,
if desired, be recovered by using the \ml{defintion} and \ml{theorem} functions
provided by \ML. Note that all theorems are printed with the interface map set
up as done by the library. In addition the symbol {\tt -->} is used for the
constants {\tt tends\_num\_real} and {\tt tends\_real\_real} in the theories
{SEQ} and {LIM} respectively.
