# How to refer to steps in TLAPS proofs? (new to TLA+)

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### Saswata Paul

Jul 5, 2019, 2:48:46 AM7/5/19
to tlaplus
In page 6 of the paper "How to write a proof" (http://lamport.azurewebsites.net/pubs/lamport-how-to-write.pdf), It has been stated that "Part 3 of the statement of step <5>2 is numbered <5>.2.3.

By that syntax, in the proof of irrationality given in Figure 5. (page 7), <1>1.1 should refer to gcd(m,n)=1. However, later in the proof of m^2=2(n^2), it says PROOF: <1>1.1 implies (m/n)^2 = 2. How can gcd(m,n)=1 imply (m/n)^2 = 2 ?

I think I am missing something subtle about the numbering of steps here (or my sleepless mind is making a silly mistake elsewhere). Any help is appreciated.

PS: the content of page 7 is given below:

### Stephan Merz

Jul 5, 2019, 3:04:03 AM7/5/19

"Step <1>1.2 and assumption <0>:2 imply that (m/n)^2 = 2"

Please note that this document precedes the design of TLAPS and that the proof has not been checked mechanically.

Regards,
Stephan

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### Saswata Paul

Jul 5, 2019, 3:14:55 AM7/5/19
This makes much more sense now. Thank you!

On Friday, July 5, 2019, Stephan Merz <stepha...@gmail.com> wrote:

"Step <1>1.2 and assumption <0>:2 imply that (m/n)^2 = 2"

Please note that this document precedes the design of TLAPS and that the proof has not been checked mechanically.

Regards,
Stephan

On 5 Jul 2019, at 08:48, Saswata Paul <paulsa...@gmail.com> wrote:

In page 6 of the paper "How to write a proof" (http://lamport.azurewebsites.net/pubs/lamport-how-to-write.pdf), It has been stated that "Part 3 of the statement of step <5>2 is numbered <5>.2.3.

By that syntax, in the proof of irrationality given in Figure 5. (page 7), <1>1.1 should refer to gcd(m,n)=1. However, later in the proof of m^2=2(n^2), it says PROOF: <1>1.1 implies (m/n)^2 = 2. How can gcd(m,n)=1 imply (m/n)^2 = 2 ?

I think I am missing something subtle about the numbering of steps here (or my sleepless mind is making a silly mistake elsewhere). Any help is appreciated.

PS: the content of page 7 is given below:

<1.PNG>

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