File: RIGHT_AND_FORALL_CONV.doc

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\DOC RIGHT_AND_FORALL_CONV

\TYPE {RIGHT_AND_FORALL_CONV : conv}

\SYNOPSIS
Moves a universal quantification of the right conjunct outwards through a
conjunction.

\KEYWORDS
conversion, quantifier, universal, conjunction.

\DESCRIBE
When applied to a term of the form {P /\ (!x.Q)}, the conversion
{RIGHT_AND_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
AND_FORALL_CONV, FORALL_AND_CONV, LEFT_AND_FORALL_CONV.

\ENDDOC