File: AND_PFORALL_CONV.doc

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\DOC AND_PFORALL_CONV

\TYPE {AND_PFORALL_CONV : conv}

\SYNOPSIS
Moves a paired universal quantification outwards through a conjunction.

\KEYWORDS
conversion, quantifier.

\LIBRARY pair

\DESCRIBE
When applied to a term of the form {(!p. t) /\ (!p. t)}, the conversion
{AND_PFORALL_CONV} returns the theorem:
{
   |- (!p. t) /\ (!p. u) = (!p. t /\ u)
}
\FAILURE
Fails if applied to a term not of the form {(!p. t) /\ (!p. t)}.

\SEEALSO
AND_FORALL_CONV, PFORALL_AND_CONV, LEFT_AND_PFORALL_CONV,
RIGHT_AND_PFORALL_CONV.

\ENDDOC