# Re: [isabelle] Proving equivalence

Actually, proving "(0::real) = 1" using that as a fact doesn't make it inconsistent, right? It just means that it has at least one unsatisfying model.
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Steve

On Jan 25, 2011 9:17pm, s.wong.731 at gmail.com wrote:
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```Hi,
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Thanks for pointing out the inconsistency. Just curious, how could you could spot the inconsistency? How could "(0::real) = 1" be derived from that axiom?
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```Thanks again
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```Steve
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```On Jan 25, 2011 6:11pm, Brian Huffman brianh at cs.pdx.edu> wrote:
> Hi Steve,
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>
>
> As Tjark pointed out recently, axioms are evil. It just so happens
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> that both of your example axiomatizations are inconsistent. As you can
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> see:
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>
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> lemma "(0::real) = 1"
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> using ax1 by metis
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>
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> (The same proof works also for ax2.)
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>
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> This might explain why metis can easily solve your lemma: because from
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> ax1 or ax2 metis can prove any equation between real numbers!
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>
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> - Brian
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>
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> On Tue, Jan 25, 2011 at 9:18 AM, Tjark Weber webertj at in.tum.de> wrote:
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> > Steve,
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> >
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> > On Tue, 2011-01-25 at 16:51 +0000, Steve W wrote:
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> >> Auto can't find a proof. How come this is so difficult for auto? What
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> >> is the proper way to do this proof?
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> >
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> > both "by blast" and "by metis" succeed. I didn't investigate why auto
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> > fails.
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> >
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> > Kind regards,
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> > Tjark
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> >
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> >
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> >
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>
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