\DOC PSELECT_ELIM
\TYPE {PSELECT_ELIM : (thm -> (term # thm) -> thm)}
\KEYWORDS
rule, epsilon.
\LIBRARY pair
\SYNOPSIS
Eliminates a paired epsilon term, using deduction from a particular
instance.
\DESCRIBE
{PSELECT_ELIM} expects two arguments, a theorem {th1}, and a pair
{(p,th2):(term # thm)}. The conclusion of {th1} must have the form {P($@
P)},
which asserts that the epsilon term {$@ P} denotes some value at which
{P} holds. The paired variable structure {p} appears only in the
assumption
{P p} of the theorem {th2}. The conclusion of the resulting theorem
matches
that of {th2}, and the hypotheses include the union of all hypotheses
of the premises excepting {P p}.
{
A1 |- P($@ P)
A2 u {{P p}} |- t
------------------------------------- PSELECT_ELIM th1 (p ,th2)
A1 u A2 |- t
}
where {p} is not free in {A2}. If {p} appears in the conclusion of
{th2}, the epsilon term will NOT be eliminated, and the conclusion will
be
{t[$@ P/p]}.
\FAILURE
Fails if the first theorem is not of the form {A1 |- P($@ P)}, or if
any of the variables from the variable structure {p} occur free in any
other assumption of {th2}.
\SEEALSO
SELECT_ELIM, PCHOOSE, SELECT_AX, PSELECT_CONV, PSELECT_INTRO,
PSELECT_RULE.
\ENDDOC