\DOC AND_EXISTS_CONV
\TYPE {AND_EXISTS_CONV : conv}
\SYNOPSIS
Moves an existential quantification outwards through a conjunction.
\KEYWORDS
conversion, quantifier.
\DESCRIBE
When applied to a term of the form {(?x.P) /\ (?x.Q)}, where {x} is free
in neither {P} nor {Q}, {AND_EXISTS_CONV} returns the theorem:
{
|- (?x. P) /\ (?x. Q) = (?x. P /\ Q)
}
\FAILURE
{AND_EXISTS_CONV} fails if it is applied to a term not of the form
{(?x.P) /\ (?x.Q)}, or if it is applied to a term {(?x.P) /\ (?x.Q)}
in which the variable {x} is free in either {P} or {Q}.
\COMMENTS
It may be easier to use higher order rewriting with some of
{BOTH_EXISTS_AND_THM}, {LEFT_EXISTS_AND_THM}, and
{RIGHT_EXISTS_AND_THM}.
\SEEALSO
Conv.EXISTS_AND_CONV, Conv.LEFT_AND_EXISTS_CONV,
Conv.RIGHT_AND_EXISTS_CONV, BOTH_EXISTS_AND_THM, LEFT_EXISTS_AND_THM,
RIGHT_EXISTS_AND_THM.
\ENDDOC