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FORALL_IMP_CONV                                                 (Conv)
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FORALL_IMP_CONV : conv

SYNOPSIS
Moves a universal quantification inwards through an implication.

KEYWORDS
conversion, quantifier, universal, implication.

DESCRIBE
When applied to a term of the form {!x. P ==> Q}, where {x} is not free in
both {P} and {Q}, {FORALL_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

is returned.  If {x} is free in {Q} but not in {P}, then the
result is:

   |- (!x. P ==> Q) = P ==> (!x.Q)

And if {x} is free in neither {P} nor {Q}, then the result is:

   |- (!x. P ==> Q) = (?x.P) ==> (!x.Q)




FAILURE
{FORALL_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
Conv.LEFT_IMP_EXISTS_CONV, Conv.RIGHT_IMP_FORALL_CONV.

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