----------------------------------------------------------------------
RIGHT_IMP_PEXISTS_CONV                                     (PairRules)
----------------------------------------------------------------------
RIGHT_IMP_PEXISTS_CONV : conv

KEYWORDS
conversion, quantifier, existential, implication.

LIBRARY
pair

SYNOPSIS
Moves a paired existential quantification of the consequent outwards through
an implication.

DESCRIBE
When applied to a term of the form {t ==> (?p. u)},
{RIGHT_IMP_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 that appear free in the input term.

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

SEEALSO
Conv.RIGHT_IMP_EXISTS_CONV, PairRules.PEXISTS_IMP_CONV,
PairRules.LEFT_IMP_PFORALL_CONV.

----------------------------------------------------------------------