Re: [tlaplus] Simple contradiction proof

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 <sillymouse333@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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