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SELECT_RULE                                                    (Drule)
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SELECT_RULE : thm -> thm

SYNOPSIS
Introduces an epsilon term in place of an existential quantifier.

KEYWORDS
rule, epsilon.

DESCRIBE
The inference rule {SELECT_RULE} expects a theorem asserting the
existence of a value {x} such that {P} holds.  The equivalent assertion
that the epsilon term {@x.P} denotes a value of {x} for
which {P} holds is returned as a theorem.

       A |- ?x. P
   ------------------  SELECT_RULE
    A |- P[(@x.P)/x]




FAILURE
Fails if applied to a theorem the conclusion of which is not
existentially quantified.

EXAMPLE
The axiom {INFINITY_AX} in the theory {ind} is of the form:

   |- ?f. ONE_ONE f /\ ~ONTO f

Applying {SELECT_RULE} to this theorem returns the following.

   - SELECT_RULE INFINITY_AX;
   > val it =
     |- ONE_ONE (@f. ONE_ONE f /\ ~ONTO f) /\ ~ONTO @f. ONE_ONE f /\ ~ONTO f
     : thm





USES
May be used to introduce an epsilon term to permit rewriting with a
constant defined using the epsilon operator.

SEEALSO
Thm.CHOOSE, Conv.SELECT_CONV, Drule.SELECT_ELIM, Drule.SELECT_INTRO.

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