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: |
|---|---|---|---|
| insert-rec-correct | proved | all subs proved | abs-sym, hash-same, disj-reduce, inv-reduce, less, size, disj-neq, at-put, hash-given, in-abs, |
| insert-correct | proved | all subs proved | less, disj-neq, hash-same, disj-reduce, size, inv-reduce, hash-given, at-put, in-abs, |
| inv-reduce | proved | all subs proved | inv, size, |
| abs-sym | proved | all subs proved | in-abs, |
| at-put | proved | all subs proved | inv, |
| hash-given | proved | all subs proved | inv, |
| size | proved | all subs proved | inv, |
| disj-reduce | proved | all subs proved | disj, |
| hash-same | proved | all subs proved | inv, |
| disj-neq | proved | all subs proved | disj, |
| less | proved | all subs proved | inv, |
| lookup-correct | proved | all subs proved | in-abs, |
| disj | axiom | ||
| inv | axiom | ||
| in-abs | axiom |