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: |
|---|---|---|---|
| Sep-weak-conjunction | proved | all subs proved | Sep-unfold, |
| Sep-unfold | proved | all subs proved | Sep-rec, Sep-split, |
| Sep-forall-reduce-imp | proved | all subs proved | Sep-forall-prove-imp, |
| Sep-split | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-forall-prove-imp | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-emp | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-distribute-true | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-forall | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-range | proved | all subs proved | Sep-rec, Sep-base, |
| Sep-base | axiom | ||
| Sep-rec | axiom |