\DOC
\TYPE {SELECT_ELIM_TAC : tactic}
\SYNOPSIS
Eliminates a Hilbert-choice ("selection") term from the goal.
\KEYWORDS
tactic, Hilbert-choice, select.
\DESCRIBE
{SELECT_ELIM_TAC} searches the goal it is applied to for terms
involving the Hilbert-choice operator, of the form {@x. ...}. If such
a term is found, then the tactic will produce a new goal, where the
choice term has disappeared. The resulting goal will require the
proof of the non-emptiness of the choice term's predicate, and that
any possible choice of value from that predicate will satisfy the
original goal.
Thus, {SELECT_ELIM_TAC} can be seen as a higher-order match against
the theorem
{
|- !P Q. (?x. P x) /\ (!x. P x ==> Q x) ==> Q ($@ P)
}
where the new goal is the antecedent of the implication. (This theorem
is {SELECT_ELIM_THM}, from theory {bool}.)
\EXAMPLE
When applied to this goal,
{
- SELECT_ELIM_TAC ([], ``(@x. x < 4) < 5``);
> val it = ([([], ``(?x. x < 4) /\ !x. x < 4 ==> x < 5``)], fn) :
(term list * term) list * (thm list -> thm)
}
the resulting goal requires the proof of the existence of a number
less than 4, and also that any such number is also less than 5.
\FAILURE
Fails if there are no choice terms in the goal.
\COMMENTS
If the choice-term's predicate is everywhere false, goals involving
such terms will be true only if the choice of term makes no difference
at all. Such situations can be handled with the use of {SPEC_TAC}.
Note also that the choice of select term to eliminate is made in an
unspecified manner.
\SEEALSO
Drule.SELECT_ELIM, Drule.SELECT_INTRO, Drule.SELECT_RULE,
Tactic.SPEC_TAC.
\ENDDOC