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RIGHT_AND_PEXISTS_CONV                                     (PairRules)
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RIGHT_AND_PEXISTS_CONV : conv

KEYWORDS
conversion, quantifier, existential, conjunction.

LIBRARY
pair

SYNOPSIS
Moves a paired existential quantification of the right conjunct outwards
through a conjunction.

DESCRIBE
When applied to a term of the form {t /\ (?p. t)}, the conversion
{RIGHT_AND_PEXISTS_CONV} returns the theorem:

   |- t /\ (?p. u) = (?p'. t /\ (u[p'/p]))

where {p'} is a primed variant of the pair {p} that does not
contain any variables free in the input term.

FAILURE
Fails if applied to a term not of the form {t /\ (?p. u)}.

SEEALSO
Conv.RIGHT_AND_EXISTS_CONV, PairRules.AND_PEXISTS_CONV,
PairRules.PEXISTS_AND_CONV, PairRules.LEFT_AND_PEXISTS_CONV.

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