I appreciated the article for emphasising memorising definitions and statement of theorems... But not for proofs. For proofs, a general outline would be sufficient.
The reason part being essentially a one or two line natural language summary of ‘why the proof works’ — something that is almost always possible and is enlightening and conducive to efficient memorisation, but that for some reason is very rarely written down explicitly.
Along the lines of your own argument: even better would be
reason0-definition-reason1-theorem-reason2-proof
The "Reason" as result is true is that it follows from the previously established axioms via logical reasoning.
Theorem: Every subspace Y of a second-countable topological space X is second-countable.
Reason: Intersecting each set in a basis for X with Y yields a basis for Y.
Proof: [formal symbolic stuff involving open sets and unions, and mentioning cardinality, etc.]
(I’m not claiming ‘reason’ is the best word for this — it probably isn’t. But it’s not the same thing as motivation.)
> The "Reason" as result is true is that it follows from the previously established axioms via logical reasoning.
One could argue this is not the reason a result is true; it’s the reason we know it’s true. The fact that true statements follow from established truths by logical reasoning is more a property of the formal system (which hopefully is sound and consistent) than it is to do with the notion of truth itself.