There are plenty of questions around here, which are proven to be right or wrong in various ways. I wonder, what one can learn from these differing ways of how to prove something, despite the fact that: The more proofs, the better.
Let's say a statement is something like a way $A\to Z$. One proof might then break this down to $$A\to B\to \cdots \to W\to Z,$$ while the other proof takes another route $$A\to \beta \to \cdots \to \omega\to Z.$$
Is there way to morph between the various ways and by that learn something about the general structure?
EDIT What is it worth to have plenty of proofs for the "$\Rightarrow$" direction, if a have only one proof for "$\Leftarrow$"?
The question is very general. Examples, are welcome.