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: |
|---|---|---|---|
| uniquelen | proved | all subs proved | nuni, app, nuni-01, ex, inone, cons, inapp, empty, unique-e, |
| unique-add | proved | all subs proved | inone, cons, not, in-append, one, empty, unique-e, unique, unique-01, |
| unique-04 | proved | all subs proved | nuni-01, nuni, |
| unique-03 | proved | all subs proved | nuni-01, nuni, |
| perm-eq | proved | all subs proved | lookup-02, unique-02, inassoc, perm-unique, |
| lenequal | proved | all subs proved | app, nuni-01, nuni, ex, inone, cons, inapp, empty, unique-e, |
| infirst | proved | all subs proved | inrec, |
| unique-01 | proved | all subs proved | inone, cons, inapp, empty, unique, |
| perm-unique | proved | all subs proved | unique-02, inassoc, unique-del, cons, unique-e, |
| nuni | proved | all subs proved | inone, cons, inapp, empty, nuni-01, |
| inrec | proved | all subs proved | in-01, inassoc, inkeys-nc, |
| unique-put | proved | all subs proved | in-put, cons, put-yes, put-no, unique-e, one, put-empty, |
| in-put | proved | all subs proved | inapp, put-yes, put-no, in-append, empty, inone, put-empty, |
| unique | proved | all subs proved | inone, inapp, cons, unique-e, one, |
| unique-del | proved | all subs proved | unique-02, inassoc, inone, inapp, cons, empty, unique-e, |
| lookup-02 | proved | all subs proved | not, in-01, assoc-no, cons, assoc-yes, unique-e, unique-02, |
| nuni-01 | proved | all subs proved | not, cons, |
| app | proved | all subs proved | inapp, cons, not, |
| inkeys-nc | proved | all subs proved | in-01, inassoc, inkeys-n, |
| lookup-append-01 | proved | all subs proved | assoc-no, inone, in-append, |
| lenle | proved | all subs proved | ex, empty, unique-e, inone, cons, inapp, |
| lastoccurrence-key | proved | all subs proved | inapp, empty, inone, in-append, |
| firstoccurrence-key | proved | all subs proved | inapp, empty, inone, in-append, |
| one | proved | all subs proved | unique-e, empty, unique-r, |
| unique-02 | proved | all subs proved | in-01, cons, |
| ex | proved | all subs proved | inassoc, inone, inapp, |
| inkeys-n | proved | all subs proved | in-01, inassoc, |
| in-append | proved | all subs proved | inapp, |
| not | proved | all subs proved | cons, |
| not-in | proved | all subs proved | in-01, |
| lookup-append | proved | all subs proved | assoc-no, assoc-yes, inone, inapp, empty, |
| lookup-01 | proved | all subs proved | assoc-no, inone, inapp, one-01, |
| lookup | proved | all subs proved | assoc-no, inone, inapp, assoc-yes, |
| insnotin | proved | all subs proved | put-no, inone, inapp, put-empty, |
| insfirst | proved | all subs proved | put-no, inone, inapp, put-yes, |
| in-assoclist-01 | proved | all subs proved | assoc-no, assoc-yes, inone, inapp, empty, |
| in-assoclist | proved | all subs proved | assoc-no, assoc-yes, inone, inapp, empty, |
| in-04 | proved | all subs proved | inone, inapp, |
| in-03 | proved | all subs proved | inapp, |
| in-02 | proved | all subs proved | inone, inapp, |
| in | proved | all subs proved | in-01, cons, |
| firstoc | proved | all subs proved | inone, inapp, empty, |
| at-put-01 | proved | all subs proved | assoc-no, assoc-yes, put-yes, put-no, one-01, put-empty, |
| at-put | proved | all subs proved | assoc-yes, assoc-no, put-yes, put-no, lookup-one, put-empty, |
| in-01 | proved | all subs proved | inassoc, |
| empty | proved | all subs proved | inassoc, |
| inone | proved | all subs proved | inassoc, |
| one-01 | proved | all subs proved | assoc-yes, |
| lookup-one | proved | all subs proved | assoc-no, |
| cons | proved | all subs proved | unique-r, |
| inapp | proved | all subs proved | inassoc, |
| put-one-01 | proved | all subs proved | put-empty, put-no, |
| put-one | proved | all subs proved | put-yes, |
| put-in | proved | all subs proved | put-yes, put-no, put-empty, |
| incons | proved | all subs proved | inassoc, |
| unique-e | axiom | ||
| inassoc | axiom | ||
| unique-r | axiom | ||
| put-empty | axiom | ||
| put-no | axiom | ||
| put-yes | axiom | ||
| assoc-no | axiom | ||
| assoc-yes | axiom |