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: |
|---|---|---|---|
| Security-simple | proved | all subs proved | lemma1, |
| Security | proved | all subs proved | lemma1, |
| lemma1 | proved | all subs proved | eqd-reflexivity, lemma1-gen, run-initial, |
| eqd-run-lemma | proved | all subs proved | eqd-transitivity, eqd-symmetry, eqd-reflexivity, lemma1-gen, |
| lemma1-gen | proved | all subs proved | step1-eqd, step-eqd, purge-rec, run-rec, purge-base, run-base, |
| purge-idempotent | proved | all subs proved | purge-rec, purge-base, |
| run-base | axiom | ||
| purge-base | axiom | ||
| run-rec | axiom | ||
| purge-rec | axiom | ||
| step-eqd | proved | all subs proved | |
| step1-eqd | proved | all subs proved | |
| run-initial | axiom | ||
| eqd-reflexivity | proved | all subs proved | |
| eqd-symmetry | proved | all subs proved | |
| eqd-transitivity | proved | all subs proved |