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[tlaplus] Operators interpretation -- leads_to

Hello all,

I've recently started working on TLA+ and came across something that I can't quite understand.

I have been experimenting with the leads_to operator. It's clear to me that F ~> G is equivalent to [] ( F => <> G ) (1)

Now, let's consider a liveness properties of the form:

\forall a \in A: (a.something = "value_1") ~> (b.something_else = "value") (2)

When expressing the same using (1), it should look like:

\forall a \in A: [] ( (a.something = "value_1") => <> (b.something_else = "value") ) (3)

Is that right?

Then another question is -- how's the following property interpreted?

[] (\forall a \in A: (a.something = "value_1") => <> (b.something_else = "value") ) (4)

which still parses, thus it's a valid TLA+ formula.

Thank you in advance,


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