Re: [tlaplus] Temporal operator leads to always (F ~> []G): misunderstanding?

Thanks! Looking at the book a bit more, it says that F ~> G is equivalent to saying that exists a behavior following of F that satisfies G. I'm can kind of see that F ~> []G doesn't quite work, but my intuition is still a bit fuzzy.
```
```
That said, from Specifying Systems (page 89) I can see that if I want to check that G remains true after the initial transition, I can add a separate temporal property:
```
TwoRemainsTwo == []((i = 2) => [](i = 2))

```
I added this to the temporal properties and TLC indeed finds a violation. However, when I combined the two conditions:
```
(i = 1) ~> (i = 2) /\ []((i = 2) => [](i = 2))

```
and checked this in TLC, it appears to find no violations again? Am I doing something wrong again?
```
Thanks,
Shuhao

On 2021-06-28 3:33 p.m., Markus Kuppe wrote:
```
```On 6/28/21 12:01 PM, Shuhao Wu wrote:
```
I've been trying to write a temporal property to check in TLC where I want to know that some condition F leads to G, and G remain true for the rest of time. This lead me to using the temporal operators ~> and [] together, in a statement in the form of F ~> []G. I'm likely misunderstanding one of these operators, as when I used TLC to check the following simple spec, the nothing was found to be violated:
```
variables i = 1;

define
\* This is the temporal property to check
OneLeadsToTwo == (i = 1) ~> [](i = 2)
end define;

begin

step1: i := 2;
step2: i := 3;
step3: i := 2;

end algorithm;

```
My understanding is that (i = 1) ~> (i = 2) would be true for the above program (which is true in TLC). In the same understanding, (i = 1) ~> [](i = 2) would not be true, as the variable i changed from 1 to 2, then away from 2, and then back to 2. This means that i = 2 is not always true following the initial transition from i = 1 to i = 2.
```
What am I missing?
```
```

```
Leads-to  (P ~> Q)  is "syntactic sugar" for  [](P => <>Q)  (see page 91 of Specifying Systems).
```
M.

```
```
--
You received this message because you are subscribed to the Google Groups "tlaplus" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx.
To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/4fc36b77-e942-2301-1beb-6c175725c88e%40shuhaowu.com.
```

• References: