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*From*: hjh2bs@xxxxxx*Date*: Wed, 4 Dec 2019 14:44:24 -0800 (PST)

Hi,

The backend provers are unable to prove the above theorem. SMT specifically times out and increasing the timeout doesn't appear to help.

will successfully prove the theorem. Are the backend provers able to work with 'CHOOSE' _expression_ in conjunction with sets? Is there anything wrong with how I'm specifying the assumption? The actual algorithm will require using the division operator with a few 'min'/'max' operators, which may also complicate the proof process, so I'm wondering if TLAPS is able to prove these sort of algorithms that require arithmetic.

-- I'm working on proving an algorithm using TLAPS that requires dividing integers by two. I understand there's no support for real numbers/division in the backend provers, so I am using an operator:

`divide_by_two(n) == CHOOSE k \in Nat: n=2*k`

The problem I'm running into is when trying to prove properties using the above operator with set expressions. The following example demonstrates this:

EXTENDS Integers, TLAPS, FiniteSets

divide_by_two(n) == CHOOSE k \in Nat: n=2*k

CONSTANTS N

VARIABLES x

Init == x = divide_by_two(N)

PositiveInvariant == x >= 0

ASSUME NumberAssumption == N \in {2,4,6,8,10}

THEOREM PositiveDivisionProperty == Init => PositiveInvariant <1> SUFFICES ASSUME Init PROVE PositiveInvariant OBVIOUS <1> QED BY NumberAssumption DEF Init, PositiveInvariant, divide_by_two

The backend provers are unable to prove the above theorem. SMT specifically times out and increasing the timeout doesn't appear to help.

Changing the assumption to:

`ASSUME NumberAssumption == N = 10`

will successfully prove the theorem. Are the backend provers able to work with 'CHOOSE' _expression_ in conjunction with sets? Is there anything wrong with how I'm specifying the assumption? The actual algorithm will require using the division operator with a few 'min'/'max' operators, which may also complicate the proof process, so I'm wondering if TLAPS is able to prove these sort of algorithms that require arithmetic.

Best,

Hans

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**Follow-Ups**:**Re: [tlaplus] Using a Division Operator with TLAPS***From:*Saksham Chand

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