File: LEFT_IMP_EXISTS_CONV.doc

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\DOC LEFT_IMP_EXISTS_CONV

\TYPE {LEFT_IMP_EXISTS_CONV : conv}

\SYNOPSIS
Moves an existential quantification of the antecedent outwards through an
implication.

\KEYWORDS
conversion, quantifier, existential, implication.

\DESCRIBE
When applied to a term of the form {(?x.P) ==> Q}, the conversion
{LEFT_IMP_EXISTS_CONV} returns the theorem:
{
   |- (?x.P) ==> Q = (!x'. P[x'/x] ==> Q)
}
\noindent where {x'} is a primed variant of {x} that does not appear free in
the input term.

\FAILURE
Fails if applied to a term not of the form {(?x.P) ==> Q}.

\SEEALSO
FORALL_IMP_CONV, RIGHT_IMP_FORALL_CONV.

\ENDDOC