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*From*: Stephan Merz <stephan.merz@xxxxxxxxx>*Date*: Mon, 18 Mar 2019 09:07:50 +0100*References*: <a6d1fe97-2abe-45fa-816b-351d34f8b3bb@googlegroups.com>

Hello, theorem proving is indeed driven by syntax and unfortunately, TLAPS's automatic backends may fail to prove lemmas that are true, even if their truth is obvious to a human. Recognizing the elements of the set expression [s:{0}] requires reasoning about the extension of the set, whereas the set { [s |-> 0] } is just a singleton whose sole element is explicitly given. I am happy to report that your lemma1 will (also) be proved by SMT in the upcoming release, as well as LEMMA lemma3 == ASSUME NEW C, NEW D, C = {[s|->0]}, D = {[s|->x.s] : x \in C} PROVE C = D OBVIOUS The proof of lemma2 currently seems to require a somewhat roundabout proof: LEMMA lemma2 == ASSUME NEW C, NEW D, C = [s : {0}], D = {[s|->x.s] : x \in C} PROVE C = {[s|->x.s] : x \in D} <1>1. C = {[s |-> 0]} OBVIOUS <1>2. QED BY ONLY <1>1, D = {[s|->x.s] : x \in C} where step <1>1 is proved by Isabelle and step <1>2 by either SMT or Isabelle (but both backends fail if the assumption about C is not hidden). Thanks for reporting this, we'll try to add a suitable rewrite rule for automating the handling of similar expressions. Stephan > On 17 Mar 2019, at 20:50, haroldas.giedra@xxxxxxxxx wrote: > > > Hello, > > I have example of two lemmas which have the same meaning but slightly differs in the syntax. > > LEMMA lemma1 == C = {[s|->0]} > /\ > D = {[s|->x.s] : x \in C} > => > C = {[s|->x.s] : x \in D} > OBVIOUS > > LEMMA lemma2 == C = [s : {0}] > /\ > D = {[s|->x.s] : x \in C} > => > C = {[s|->x.s] : x \in D} > OBVIOUS > > lemma1 has been proved by "TLA - Isabelle", but "TLA - SMT", "TLA - Zenon", "TLA - Isabelle" fail to prove lemma2. > > I don't understand why TLA proof system fails to prove lemma2, which is different from lemma1 only in the syntax of TLA records. Meaning: > > C = {[s|->0]} > and > C = [s : {0}] > > which are the same for me. > > Harold > > -- > You received this message because you are subscribed to the Google Groups "tlaplus" group. > To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. > To post to this group, send email to tlaplus@xxxxxxxxxxxxxxxx. > Visit this group at https://groups.google.com/group/tlaplus. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To post to this group, send email to tlaplus@xxxxxxxxxxxxxxxx. Visit this group at https://groups.google.com/group/tlaplus. For more options, visit https://groups.google.com/d/optout.

**Follow-Ups**:**Re: [tlaplus] TLA Proof System - the syntax has impact on provability ?***From:*haroldas . giedra

**References**:**[tlaplus] TLA Proof System - the syntax has impact on provability ?***From:*haroldas . giedra

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