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*From*: Stephan Merz <stephan.merz@xxxxxxxxx>*Date*: Mon, 29 Jul 2019 10:29:00 +0200*References*: <73c9e238-d51f-4f38-b7dd-4137fe456fc9@googlegroups.com>

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 > > -- > 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/73c9e238-d51f-4f38-b7dd-4137fe456fc9%40googlegroups.com. -- 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/D0F9634B-B11F-43F6-BFEC-05B1B15B2677%40gmail.com.

**References**:**[tlaplus] Proving INV1***From:*aric . nappi

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