File: EXISTS_IMP.doc

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\DOC EXISTS_IMP

\TYPE {EXISTS_IMP : (term -> thm -> thm)}

\SYNOPSIS
Existentially quantifies both the antecedent and consequent of an implication.

\KEYWORDS
rule, quantifier, existential, implication.

\DESCRIBE
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.

\SEEALSO
EXISTS_EQ.

\ENDDOC