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# Re: [tlaplus] Proving INV1

```Hello,

from the hypothesis of INV1

I /\ [N]_f => I'

you can derive both

(1) [N]_f => [I => I']_f    and    (2) I /\ f'=f => I'

by propositional logic. Now, apply TLA1 to (1), with P and Q both TRUE, to derive

(3) [][N]_f => [][I => I']_f

(If you are really meticulous, use STL1 to get rid of the formula []TRUE on the left-hand side of the direct conclusion of TLA2.) From (2), TLA1 gives you

(4) []I <=> I /\ [][I => I']_f

and the conclusion of INV1 follows from (3) and (4).

Regards,
Stephan

> On 25 Jul 2019, at 14:52, aric.nappi@xxxxxxxxx wrote:
>
> Hi all, I am reading Mr. Lamport's paper The Temporal Logic of Actions [0]. In section 5.6 of that paper, he lays out the proof rules of simple temporal logic and simple TLA. I managed to prove the validity of STL1-6 and Lattice and I have proven TLA1 and TLA2 using the previous rules, but I am stuck trying to prove INV1, which is
>
> I /\ [N]_f => I'
> -------------------
> I /\ [][N]_f => []I
>
> where I is a predicate, N is an action, and f is a state function.
>
> I was thinking that you need to use either TLA1 or TLA2, but I have not had much luck. If anyone could point me in the right direction, such as by letting me know which proof rules are important in proving this rule, I would be grateful.
>
> Thanks
>
>
>
> [0] http://lamport.azurewebsites.net/pubs/pubs.html#lamport-actions
>
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```