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Re: [tlaplus] WITNESS BY



To expand on Stephan's reply, the SUFFICES keyword is actually optional in SUFFICES steps. So just writing an _expression_ without any keyword prepended is writing a SUFFICES step.

Andrew

On Sunday, November 20, 2022 at 3:16:56 AM UTC-5 Stephan Merz wrote:
Hi Jaco,

the directive "WITNESS e" quite clearly does not require proof, and by analogy (and in order to simplify the grammar) it was decided that "WITNESS e \in S" would not take a proof either but that the fact "e \in S" should follow obviously from the context. What you can do is write something like the following where the first step inserts the required fact in the context.

<1>. e \in S
  BY ...
<1>. WITNESS e \in S

Personally, I tend to use WITNESS rarely but usually write something like

<1>x. e \in S
  BY ...
<1>y. P(e)
  BY ...
<1>z. \E x \in S : P(x)
  BY <1>x, <1>y

Regards,
Stephan


On 19 Nov 2022, at 14:15, Jaco van de Pol <jaco...@xxxxxxxxx> wrote:

Hi,
My "WITNESS x \in y" generates a proof obligation, so it would be nice to
write WITNESS x\in y BY <proof>, but as far as I understand this is not
possible. Is there a reason? Is there a general work around?
Thanks for your thoughts,
Jaco van de Pol

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