relation of inference rules to axioms and proofs
Published 2020-08-27T22:01:00.003Z by Physics Derivation Graph
Axioms are a set of statements upon which other statements can be formed.
Lemmas are easy but irrelevant.
Corollaries are quick but irrelevant consequences
Propositions are interesting
Theorems are important and difficult
A proof is about consistency of statements with respect to a set of axioms.
To show the connection can be made, pick the simplest PDG inference rules.
* "add X to both sides"
* "multiply both sides by"