Prove that `real.pi` is irrational using [Niven's argument](https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-53/issue-6/A-simple-proof-that-pi-is-irrational/bams/1183510788.full), see also [Wikipedia](https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Niven's_proof) [Zulip](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Paulson's.20.22small.20formalisation.20challenges.22)
Prove that
real.piis irrational using Niven's argument, see also WikipediaZulip