Moves a universal quantification inwards through an 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.