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: |
|---|---|---|---|
| inf-unique | proved | all subs proved | lowerbound-def, boundedge-def, |
| boundedge-neg-boundedle | proved | all subs proved | upperbound-def, boundedle-def, lowerbound-def, boundedge-def, |
| lowbound-neg-upperbound | proved | all subs proved | upperbound-def, lowerbound-def, |
| inf-exists | proved | all subs proved | upperbound-def, boundedle-def, sup-exists, lowerbound-def, boundedge-def, |
| sup-unique | proved | all subs proved | upperbound-def, boundedle-def, |
| inf-neg-sup | proved | all subs proved | sup-upperbound, inf-highest-lowerbound, inf-lowerbound, upperbound-def, boundedle-def, sup-lowest-upperbound, lowerbound-def, boundedge-def, |
| sup-lowest-upperbound | axiom | ||
| inf-lowerbound | axiom | ||
| inf-highest-lowerbound | axiom | ||
| sup-upperbound | axiom | ||
| sup-exists | axiom | ||
| boundedle-def | axiom | ||
| upperbound-def | axiom | ||
| boundedge-def | axiom | ||
| lowerbound-def | axiom |