Existentially quantifies both the antecedent and consequent of an implication.
DESCRIPTION
When applied to a variable x and a theorem A |- t1 ==> t2, the
inference rule EXISTS_IMP returns the theorem A |- (?x. t1) ==> (?x. t2),
provided x is not free in the assumptions.
A |- t1 ==> t2
-------------------------- EXISTS_IMP "x" [where x is not free in A]
A |- (?x.t1) ==> (?x.t2)
FAILURE
Fails if the theorem is not implicative, or if the term is not a variable, or
if the term is a variable but is free in the assumption list.