[tsimionescu]

But does this do anything meaningful, or is it just pointless drudgery because Coq is a machine and can't 'understand'/assume even simple maths/logic if it isn't explicitly stated? This is not a slight on Coq by any means, just pointing out the difference between human proofs and machine proofs. (Humans can of course be tricked into thinking that subtly false statements are trivially true, which the much more meticulous machine proof would discover)

That is, what is being gained by looking at the vacuously true cases where n<2, when the only interesting base case is the one where the LHS of the implication is true?

[eperdew]

I wrote out quite a bit for this, but I think that the main point is that by falling back to the formalism, we see the the LHS of the implication affects our inductive hypothesis. I think this is something that is not clear if you just do "base case starting at n" style proofs."

As far as drudgery, Coq will solve the trivial cases automatically, so you'd never have to prove the n = 0 case by hand. That said, there's a reason most math is done on paper and not in Coq - there's usually an order of magnitude more detail and drudgery in a formal proof, even with automation.