Re: [tlaplus] Q about the existential quantifier

Hello,

the implication

[](\E x : F) => \EE x : []F

is indeed valid. The reverse implication need not hold. For example,

\EE x : []<> << x' # x >>_x

is valid, but

[] \E x : <> << x' # x >>_x

is a contradiction. If F is a state predicate then

(\EE x : []F) => [](\E x : F)

is valid.

Stephan

On 29 May 2021, at 05:51, ns <nedsri1988@xxxxxxxxx> wrote:

hello, the Specifying Systems book says that a regular existentially quantified variable functions as a constant. And from the definition this does seem to be the case
\sigma |= (\E x: F) == \E x: (\sigma |= F)
where \sigma is a trace. However, if I have
[] (\E x: F)
its now possible for each state of \sigma to have a different value of x and satisfy this formula. But this now seems closer to a temporal existential. So would it be equivalent to
\EE x: [] F
?
thanks

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