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

On 18 Feb 2022, at 16:23, Алексей Тимаков <timakov.alan@xxxxxxxxx> wrote:

Hi. Thanks a lot. I will use ASSUME for a while. The example i provided is a simplified version of a real one ).

четверг, 17 февраля 2022 г. в 10:32:39 UTC+3, Stephan Merz:
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 <timako...@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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