File: RIGHT_IMP_FORALL_CONV.doc

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\DOC RIGHT_IMP_FORALL_CONV

\TYPE {RIGHT_IMP_FORALL_CONV : conv}

\SYNOPSIS
Moves a universal quantification of the consequent outwards through an
implication.

\KEYWORDS
conversion, quantifier, universal, implication.

\DESCRIBE
When applied to a term of the form {P ==> (!x.Q)}, the conversion
{RIGHT_IMP_FORALL_CONV} returns the theorem:
{
   |- P ==> (!x.Q) = (!x'. P ==> (Q[x'/x]))
}
\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 {P ==> (!x.Q)}.

\SEEALSO
FORALL_IMP_CONV, LEFT_IMP_EXISTS_CONV.

\ENDDOC