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*From*: Andrew Helwer <andrew.helwer@xxxxxxxxx>*Date*: Wed, 29 Mar 2023 10:23:23 -0700 (PDT)*References*: <CABj=xUW4ayrmf+sVxViXOmpj0QSGb=vRCpUwmqn=1QVygirEOQ@mail.gmail.com> <30EB506E-5FC5-4B2C-B21D-EB577C63BEA6@gmail.com>

Thanks, Stephan! I was stuck with tlapm not proving the final QED step, removing the SUFFICES step fixed it.

Andrew

On Wednesday, March 29, 2023 at 12:49:26 PM UTC-4 Stephan Merz wrote:

The error message says:Non-constant TAKE, WITNESS, or HAVE for temporal goalso this restriction was an explicit design decision. (Not sure if it is documented anywhere ...)Even with the explicit SUFFICES construct, your proof is likely to be doomed: at some point you'll have to apply temporal logic reasoning (the PTL method), and as a rule of thumb, in all temporal steps the context should only contain "boxed" assumptions, i.e., all assumptions A should be equivalent to []A. This is true for constant formulas A, formulas []A, <>[]A, WF_v(A) etc., but not for Spec, which will contain an initial state predicate.If you continue your proof attempt, you'll find that PTL warns about "non-[] assumption" and fails. Invariant proofs should be written in the formTHEOREM Spec => []Invariant<1>1. Init => Invariant<1>2. Invariant /\ [][Next]_v => Invariant'<1>. QED BY <1>1, <1>2, PTL DEF SpecIn particular, the context of the QED step is empty, so all its assumptions are "boxed".StephanOn 29 Mar 2023, at 18:16, Andrew Helwer <andrew...@xxxxxxxxx> wrote:I ran into this error when writing theorems like:THEOREM Spec => []InvariantPROOF<1> HAVE Spec<1> ...<1> QEDIf I replace it with this then SANY stops complaining:THEOREM Spec => []InvariantPROOF<1> SUFFICES ASSUME Spec PROVE []Invariant OBVIOUS<1> ...<1> QEDWhy is the second one okay but the first one is not? I thought the first one was just shorthand for the second.Andrew--

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**Follow-Ups**:**Re: [tlaplus] SANY error: Non-constant TAKE, WITNESS, or HAVE for temporal goal.***From:*Andrew Helwer

**References**:**[tlaplus] SANY error: Non-constant TAKE, WITNESS, or HAVE for temporal goal.***From:*Andrew Helwer

**Re: [tlaplus] SANY error: Non-constant TAKE, WITNESS, or HAVE for temporal goal.***From:*Stephan Merz

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