Re: [tlaplus] Simple contradiction proof

[jack malkovick <sillymouse333@xxxxxxxxx>]

Yes, it makes sense, I tried that too before...

I guess I was looking for a way to formulate a theorem in such a way it will be unprovable having an inconsistent set of facts.

Would that make any sense?

On Wednesday, November 30, 2022 at 11:04:37 AM UTC+2 Stephan Merz wrote:

Hi,

could you explain why you are surprised? The theorem holds for two reasons: (i) the assertion (TRUE) is trivial, and (ii) the assumptions are contradictory, as you say. From contradictory assumptions, anything can be proved, and in fact the following also passes:

THEOREM

    ASSUME 
        NEW P(_), 
        \A p : P(p),
        \A p : ~P(p) 
    PROVE

        FALSE
OBVIOUS

Regards,
Stephan

On 30 Nov 2022, at 09:53, jack malkovick <sillym...@xxxxxxxxx> wrote:

I just started reading about TLAPS and I tried for fun the following silly thing

THEOREM T ==
    ASSUME
        NEW P(_),
        \A p : P(p),
        \A p : ~P(p)
    PROVE
        TRUE
    PROOF
        OBVIOUS

To my surprise, the result was green. I hoped that somehow it would "detect" the contradictions in the assumptions. 

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