[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: [tlaplus] simple toy theorem



I think this is a matter of parsing precedence.

  \A x : M(x) = S(x) /\ ~U(x)

is parsed as

  \A x : (M(x) = S(x)) /\ ~U(x)

and therefore your hypotheses imply

   \A x : ~ U(x)

For the analogous reason, the hypothesis

  NEW B(_), \A x : B(x) = S(x) /\ U(x)

asserts

  \A x : U(x)

and now you get an inconsistent set of assumptions. Had you used "<=>" instead of "=", the result would have been different because conjunction binds more tightly than equivalence.

Stephan

On 30 Nov 2022, at 11:26, jack malkovick <sillymouse333@xxxxxxxxx> wrote:

Let's say we have this simple theorem

THEOREM T ==
    ASSUME
        NEW NEW S(_), NEW U(_), NEW M(_), NEW P(_),
        \A x : M(x) = S(x) /\ ~U(x),
        \A x : P(x) = M(x)
   PROVE
        \A x : P(x) => S(x)
   PROOF
        OBVIOUS

It is true.
If I negate the goal to \E x : ~(P(x) => S(x)) same as \E x : P(x) /\ ~S(x) it becomes red.

However, if I add another assumption
NEW B(_), \A x : B(x) = S(x) /\ U(x),
The theorem turns green! How can this new assumption make the theorem true?


--
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/4db36d5e-1661-43f3-a34c-89923ede385en%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/81603491-C40C-4B21-854F-71FE85158AE9%40gmail.com.