SELECT_RULE : thm -> thm

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

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;
   |- ONE_ONE(@f. ONE_ONE f /\ ~ONTO f) /\ ~ONTO(@f. ONE_ONE f /\ ~ONTO f)

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

SEEALSO  CHOOSE,   SELECT_AX,   SELECT_CONV,   SELECT_ELIM,   SELECT_INTRO

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