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: