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\DOC EXISTS_IMP_CONV
\TYPE {EXISTS_IMP_CONV : conv}
\SYNOPSIS
Moves an existential quantification inwards through an implication.
\KEYWORDS
conversion, quantifier, existential, implication.
\DESCRIBE
When applied to a term of the form {?x. P ==> Q}, where {x} is not free in
both {P} and {Q}, {EXISTS_IMP_CONV} returns a theorem of one of three forms,
depending on occurrences of the variable {x} in {P} and {Q}. If {x} is free
in {P} but not in {Q}, then the theorem:
{
|- (?x. P ==> Q) = (!x.P) ==> Q
}
\noindent is returned. If {x} is free in {Q} but not in {P}, then the
result is:
{
|- (?x. P ==> Q) = P ==> (?x.Q)
}
\noindent And if {x} is free in neither {P} nor {Q}, then the result is:
{
|- (?x. P ==> Q) = (!x.P) ==> (?x.Q)
}
\FAILURE
{EXISTS_IMP_CONV} fails if it is applied to a term not of the form
{?x. P ==> Q}, or if it is applied to a term {?x. P ==> Q} in which the
variable {x} is free in both {P} and {Q}.
\SEEALSO
LEFT_IMP_FORALL_CONV, RIGHT_IMP_EXISTS_CONV.
\ENDDOC
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