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: |
|---|---|---|---|
| sum-zero | proved | all subs proved | sum-listlength-one, |
| prod-last | proved | all subs proved | prod-one, prod-app, |
| prod-eq-one | proved | all subs proved | prod-eq-one-01, |
| sum-listlength-one | proved | all subs proved | sum-empty, sum-rec, |
| prod-app | proved | all subs proved | prod-rec, prod-empty, |
| prod-one | proved | all subs proved | prod-empty, prod-rec, |
| prod-eq-one-01 | proved | all subs proved | prod-rec, prod-empty, |
| sum-append | proved | all subs proved | sum-rec, sum-empty, |
| prod-eq-zero | proved | all subs proved | prod-rec, prod-empty, |
| sum-empty | axiom | ||
| sum-rec | axiom | ||
| prod-empty | axiom | ||
| prod-rec | axiom |