\DOC FUN_EQ_CONV
\TYPE {FUN_EQ_CONV : conv}
\SYNOPSIS
Equates normal and extensional equality for two functions.
\KEYWORDS
conversion, extentionality.
\DESCRIBE
The conversion {FUN_EQ_CONV} embodies the fact that two functions are
equal
precisely when they give the same results for all values to which they
can be
applied. When supplied with a term argument of the form {f = g}, where
{f} and
{g} are functions of type {ty1->ty2}, {FUN_EQ_CONV} returns the theorem:
{
|- (f = g) = (!x. f x = g x)
}
where {x} is a variable of type {ty1} chosen by the conversion.
\FAILURE
{FUN_EQ_CONV tm} fails if {tm} is not an equation {f = g}, where {f} and
{g}
are functions.
\USES
Used for proving equality of functions.
\SEEALSO
Drule.EXT, Conv.X_FUN_EQ_CONV.
\ENDDOC