Re: [tlaplus] proving a property of some predefined set item

[Stephan Merz <stephan.merz@xxxxxxxxx>]

Hello,

tuple declarations will soon be supported, apologies for the long wait!

However, in your example, they are unnecessary: you can simply write

LEMMA LEM1 ==  ASSUME NEW S1, NEW S2,
                      NEW Set \in SUBSET (S1 \X S2),
                      NEW p \in Set
                      PROVE  p[1] \in S1
               OBVIOUS

which is equivalent, and proved.

Regards,

Stephan

On 16 Feb 2022, at 22:21, Алексей Тимаков <timakov.alan@xxxxxxxxx> wrote:

Hi all.
I'm a newbie on TLAPS and need some help.
Can not manage to prove a simple fact

LEMMA LEM1 ==  ASSUME NEW S1, NEW S2,
                      NEW Set \in SUBSET {<<x, y>> : x \in S1, y \in S2},
                      NEW p \in Set
                      PROVE  p[1] \in S1
               OBVIOUS

Set of tuples is not supported.

However

LEMMA LEM2 ==  ASSUME NEW S1,
                      NEW Set \in SUBSET {x : x \in S1},
                      NEW p \in Set
                      PROVE  p \in S1
               OBVIOUS

works.

Should we accept LEMMA1 as an axiom?

Thanks in advance.

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