A lemma (entry) may depend on lemmas (entries) below its position, but never on lemmas above its position. This means the list is a topological order of the dependency graph. An entry 'all subs proved' means that all used lemmas are (transitively) proved.
| Name: | Status: | Subs proved? | Used: |
|---|---|---|---|
| ks-K | proved | all subs proved | ks-K-01, ks-rec, ks-zero, |
| ks-K-01 | proved | all subs proved | ks-K-02, ks-rec, ks-zero, |
| ks-not-S | proved | all subs proved | hasS-S, hasS-A, ks-not-hasS, |
| ks-not-S-01 | proved | all subs proved | hasS-S, hasS-A, ks-not-hasS, |
| ks-not-S-02 | proved | all subs proved | ks-zero, ks-rec-01, ks-not-hasS, |
| ks-K-02 | proved | all subs proved | ks-rec, ks-zero, |
| ks-rec-01 | proved | all subs proved | ks-rec, |
| ks-not-hasS | proved | all subs proved | hasS-A, ks-rec, hasS-K, ks-zero, |
| hasS-K | axiom | ||
| hasS-A | axiom | ||
| hasS-S | axiom | ||
| ks-zero | axiom | ||
| ks-rec | axiom |