File: NOT_PFORALL_CONV.doc

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\DOC NOT_PFORALL_CONV

\TYPE {NOT_PFORALL_CONV : conv}

\SYNOPSIS
Moves negation inwards through a paired universal quantification.

\KEYWORDS
conversion, quantifier, universal, negation.

\LIBRARY pair

\DESCRIBE
When applied to a term of the form {~(!p. t)}, the conversion
{NOT_PFORALL_CONV} returns the theorem:
{
   |- ~(!p. t) = (?p. ~t)
}
\noindent It is irrelevant whether any variables in {p} occur free in {t}.

\FAILURE
Fails if applied to a term not of the form {~(!p. t)}.

\SEEALSO
NOT_FORALL_CONV, PEXISTS_NOT_CONV, PFORALL_NOT_CONV, NOT_PEXISTS_CONV.

\ENDDOC