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SET_SPEC_CONV                                            (pred_setLib)
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SET_SPEC_CONV : conv

SYNOPSIS
Axiom-scheme of specification for set abstractions.

LIBRARY
pred_set

DESCRIBE
The conversion {SET_SPEC_CONV} expects its term argument to be an assertion of
the form {t IN {E | P}}. Given such a term, the conversion returns a
theorem that defines the condition under which this membership assertion holds.
When {E} is just a variable {v}, the conversion returns:

   |- t IN {v | P} = P[t/v]

and when {E} is not a variable but some other expression, the theorem
returned is:

   |- t IN {E | P} = ?x1...xn. (t = E) /\ P

where {x1}, ..., {xn} are the variables that occur free both in
the expression {E} and in the proposition {P}.

EXAMPLE

- SET_SPEC_CONV ``12 IN {n | n > N}``;
|- 12 IN {n | n > N} = 12 > N

- SET_SPEC_CONV ``p IN {(n,m) | n < m}``;
|- p IN {(n,m) | n < m} = (?n m. (p = n,m) /\ n < m)


FAILURE
Fails if applied to a term that is not of the form  {t IN {E | P}}.

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