Formal knowledge
Theorem
A proposition accepted with a proof under stated assumptions.
Definition
Theorem
A theorem is a declared proposition whose proof has been accepted by the applicable proof rules.
A theorem record should identify its exact statement, proof route, assumptions, and dependencies. Different formal systems may state related mathematics using different definitions.
01
Example
The theorem n + 0 = n for natural numbers depends on how natural numbers and addition are defined.
02
Important distinction
A theorem name or prose summary is not a substitute for its formal statement.
After reading this article, you should be able to
- Define Theorem in the sense used on this site.
- Identify the statement, assumptions, and proof route needed to interpret a theorem record.