Re: [tlaplus] on tlaps semantics

[Stephan Merz <stephan.merz@xxxxxxxxx>]

Hello,

for me both of your theorems are proved (by the SMT backend). Can you use SMT to prove simple theorems such as

THEOREM

   ASSUME NEW x \in Int

   PROVE x+1 = 1+x

   OBVIOUS

or do you perhaps have a problem with your TLAPS installation?

Regards,

Stephan

On 24 Mar 2022, at 16:45, Алексей Тимаков <timakov.alan@xxxxxxxxx> wrote:

Hi all

Can anyone tell me why this assumption cannot be proved.

THEOREM TEST4 == ASSUME NEW P1, NEW P2, NEW pred1 (_,_), NEW l, NEW pred2(_),
                        l =  {x \in {pred1(c1, c2) : c1 \in P1, c2 \in P2} : pred2(x)}
                        PROVE \A l1 \in l : \E s1 \in P1, s2 \in P2 : l1 = pred1(s1, s2)
                 PROOF OBVIOUS  

or even

THEOREM TEST2 == ASSUME NEW P1, NEW P2, NEW pred1 (_,_), NEW l,
                        l =  {pred1(c1, c2) : c1 \in P1, c2 \in P2}
                        PROVE \A l1 \in l : \E s1 \in P1, s2 \in P2 : l1 = pred1(s1, s2)
                 PROOF OBVIOUS   

Thanks.

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