Questions about TLA+ formula.

[宏黄]

Hi all.

I'm reading the TLA+ hyperbook ，And I met some questions.

In Chapter 17 Temporal Logic Question 17.5

How to prove []p=>p' is not equivalent to any legal TLA+ formula.

and  in Chapter 17.4.1 lead to 

How to understand  F~>false,i think it is nerver true,when F is true,false do not become true

[Stephan Merz]

Hello,

> On 25 Apr 2022, at 04:26, 宏黄 <wpk...@gmail.com> wrote:
>
> Hi all.
> I'm reading the TLA+ hyperbook ，And I met some questions.
> In Chapter 17 Temporal Logic Question 17.5
> How to prove []p=>p' is not equivalent to any legal TLA+ formula.

hint: all temporal formulas of TLA+ are insensitive to inserting or removing stuttering steps.

> and in Chapter 17.4.1 lead to
> How to understand F~>false,i think it is nerver true,when F is true,false do not become true

F ~> FALSE asserts that if F ever becomes true, then FALSE must be true eventually. Since the latter is impossible, the formula expresses that F can never become true. You would normally write this as []~F, but the formulation using leads-to is more convenient in the context of reasoning about leads-to properties.

Hope this helps,
Stephan

[宏黄]

 thanks very much for your answer.