\DOC EXISTS_UNIQUE_CONV
\TYPE {EXISTS_UNIQUE_CONV : conv}
\SYNOPSIS
Expands with the definition of unique existence.
\KEYWORDS
conversion, quantifier, existential, unique.
\DESCRIBE
Given a term of the form {"?!x.P[x]"}, the conversion
{EXISTS_UNIQUE_CONV}
proves that this assertion is equivalent to the conjunction of two
statements,
namely that there exists at least one value {x} such that {P[x]}, and
that
there is at most one value {x} for which {P[x]} holds. The theorem
returned is:
{
|- (?! x. P[x]) = (?x. P[x]) /\ (!x x'. P[x] /\ P[x'] ==> (x = x'))
}
where {x'} is a primed variant of {x} that does not appear free in
the input term. Note that the quantified variable {x} need not in fact
appear
free in the body of the input term. For example, {EXISTS_UNIQUE_CONV
"?!x.T"}
returns the theorem:
{
|- (?! x. T) = (?x. T) /\ (!x x'. T /\ T ==> (x = x'))
}
\FAILURE
{EXISTS_UNIQUE_CONV tm} fails if {tm} does not have the form {"?!x.P"}.
\SEEALSO
Conv.EXISTENCE.
\ENDDOC