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-eq | proved | all subs proved | Sep-forall, |
| Sep-forall | proved | all subs proved | Sep-ins, Sep-emp, |
| Sep-unfold | proved | all subs proved | Sep-ins, |
| And-forall | proved | all subs proved | And-ins, And-emp, |
| precise-Sep | proved | all subs proved | Sep-ins, Sep-emp, |
| And-discard | proved | all subs proved | And-emp, And-ins, |
| And-unfold | proved | all subs proved | And-ins, |
| And-emp | axiom | ||
| Sep-emp | axiom | ||
| Sep-ins | axiom | ||
| And-ins | axiom |