[ add ] proof of Carette's Lemma for relation m ≡ n (mod o) for {{NonZero o}}

[jamesmckinna]

Taken from the discussion at https://agda.zulipchat.com/#narrow/channel/264623-stdlib/topic/suc.20injective.20under.20_.25_/with/582024092 :

• introduces definition m ≲%[ o ] n = ∃ λ k → n ≡ m + k * o
• characterises the relation m % o ≡ n % o in terms of (the symmetric closure of) m ≲%[ o ] n
• gives two proofs of 'Carette's Lemma' (suc m) % o ≡ (suc n) % o → m % o ≡ n % o
  • indirect, via the characterisation
  • direct, via a slick proof due to @alexarice

Possible TODO:

• prove that _≲%[ o ]_ satisfies IsPreorder _≡_, indeed IsPartialOrder _≡_ etc. (decidable, ...)
• relate this to Modular arithmetic in terms of ideals #2729 and friends, esp. Create a version of [m+kn]%n≡m%n for integers #2877

[jamesmckinna]

It seems as though this should be refactorable in terms of SymClosure.(g)fold but I don't quite see it right now.