I thought I’d attempt to come up with a consistent convention of classifying mathematical statements. To do so we will simply think of the collection of statements as a partially ordered set where is interpreted as . And for each statement/node/point there will be two -valued functions that represent the number of incoming and outgoing edges (i.e. immediate antecedents and consequences). A point will be called a corollary if it has one incoming edge. A point will be called a theorem if its set of successors is a “large” subset of the poset (even if it is a corollary). A point will be called a lemma if at least one of its immediate successors is a theorem. A point will be called an axiom if it has zero incoming edges. And a point will be called a proposition if it is none of the above.
Lemmas, Theorems, Corollaries, and Propositions