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: |
|---|---|---|---|
| below-empty-rem-empty | proved | all subs proved | below-rem-in, below-rem-notin, |
| below-rem-notin | proved | all subs proved | in-below, |
| below-rem-in | proved | all subs proved | in-below, |
| in-used | proved | all subs proved | in-used-h, used-ecs, |
| in-free | proved | all subs proved | in-free-h, free-ecs, |
| below-nonempty | proved | all subs proved | in-below, |
| in-used-h | proved | all subs proved | used-ecs-rec, used-ecs-base, |
| in-free-h | proved | all subs proved | free-ecs-rec, free-ecs-base, |
| in-below | proved | all subs proved | below-rec, below-base, |
| same-used2-idexpt | proved | all subs proved | same-used, |
| same-used-same | proved | all subs proved | same-used, |
| same-used-idexpt | proved | all subs proved | same-used, |
| same-used-extract | proved | all subs proved | same-used, |
| same-used | axiom | ||
| used-ecs-base | axiom | ||
| used-ecs-rec | axiom | ||
| used-ecs | axiom | ||
| free-ecs-base | axiom | ||
| free-ecs-rec | axiom | ||
| free-ecs | axiom | ||
| below-base | axiom | ||
| below-rec | axiom |