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: |
|---|---|---|---|
| disjoint-union-empty | proved | all subs proved | union-in, union-at-left, union-right-empty, |
| union-right-empty | proved | all subs proved | union-at-left, union-in, |
| union-move-left | proved | all subs proved | union-in, union-at-left, |
| union-left-empty | proved | all subs proved | union-at-left, union-in, |
| disjoint-right-empty | proved | all subs proved | disjoint, |
| disjoint-move-left | proved | all subs proved | disjoint, |
| disjoint-left-empty | proved | all subs proved | disjoint, |
| disjoint-in-right | proved | all subs proved | disjoint, |
| disjoint-in-left | proved | all subs proved | disjoint, |
| union-at-left | axiom | ||
| union-in | axiom | ||
| disjoint | axiom |