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: |
|---|---|---|---|
| split-uni | proved | all subs proved | disj, uni, apply, |
| sep | proved | all subs proved | uni, at-unir, at-unil, at-mk, in-mk, in-uni, disj, mk-exists, apply, |
| uni | proved | all subs proved | at-unir, at-unil, at-mk, in-mk, in-uni, |
| at-unil | proved | all subs proved | at-mk, in-mk, disj, in-uni, |
| at-unir | proved | all subs proved | at-mk, in-mk, disj, in-uni, |
| mk-ext | proved | all subs proved | mk-exists, apply, |
| mk-exists | proved | all subs proved | at-mk, in-mk, emp, |
| in-uni | proved | all subs proved | in-mk, disj, |
| mapex-in0 | proved | all subs proved | mapex-in, apply, |
| mapex-del | proved | all subs proved | del, apply, |
| map-putrev | proved | all subs proved | in-mk, apply, write, |
| map-put | proved | all subs proved | in-mk, write, apply, |
| at-rw0 | proved | all subs proved | at-rw, apply, |
| mapex-put | proved | all subs proved | at-mk, in-mk, write, apply, |
| map-del | proved | all subs proved | at-mk, in-mk, del, apply, |
| map-in0 | proved | all subs proved | map-in, apply, |
| emp | proved | all subs proved | in-mk, |
| mapex-in | proved | all subs proved | at-mk, in-mk, apply, |
| at-rw | proved | all subs proved | at-mk, in-mk, apply, |
| write | proved | all subs proved | at-mk, in-mk, |
| del | proved | all subs proved | at-mk, in-mk, |
| map-in | proved | all subs proved | at-mk, in-mk, apply, |
| disj | proved | all subs proved | in-mk, |
| true-elim | proved | all subs proved | apply, |
| prop-true | proved | all subs proved | apply, |
| prop-emp | proved | all subs proved | apply, |
| mapex-new | proved | all subs proved | at-mk, in-mk, apply, |
| ex1-shift | proved | all subs proved | apply, |
| mapex-elim | proved | all subs proved | apply, |
| prop | proved | all subs proved | apply, |
| ex2-shift | proved | all subs proved | apply, |
| prop-false | proved | all subs proved | apply, |
| true-emp | proved | all subs proved | apply, |
| ex3-shift | proved | all subs proved | apply, |
| prop-sep | proved | all subs proved | apply, |
| apply | axiom | ||
| in-mk | axiom | ||
| at-mk | axiom |