Introduces an epsilon term in place of an existential quantifier.
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
A |- P[(@x.P)/x]
Fails if applied to a theorem the conclusion of which is not
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 : thm =
|- ONE_ONE (@f. ONE_ONE f /\ ~ONTO f) /\ ~ONTO (@f. ONE_ONE f /\ ~ONTO f)
May be used to introduce an epsilon term to permit rewriting with a
constant defined using the epsilon operator.