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: |
|---|---|---|---|
| prop-emp | proved | all subs proved | prop, and, and-com, and-ass, sep-com, sep-ass, emp-sep, prop-shift, |
| prop-shift | proved | all subs proved | prop-sep, and-imp, sep-com, sep-ass, and-com, and-ass, prop, and, |
| and-combine | proved | all subs proved | and, and-com, and-ass, precise-and, precise-split-l, sep-com, |
| and-split | proved | all subs proved | and, split-union, precise-split-l, sep, and-imp, sep-com, sep-ass, and-com, and-ass, |
| precise-split-r | proved | all subs proved | precise-split-l, sep-com, sep-ass, split-union, |
| septract-given | proved | all subs proved | precise-split-l, septract, Imp, |
| true-true | proved | all subs proved | true-emp, true-rev, prop, true, |
| precise-and | proved | all subs proved | precise-same, and-com, and-ass, and, precise, |
| prop-sep | proved | all subs proved | sep-com, sep-ass, split-union, and-com, and-ass, prop, and, sep, |
| and-imp | proved | all subs proved | sep-com, sep-ass, split-union, and-com, and-ass, and, sep, |
| precise-split-l | proved | all subs proved | sep, precise, sep-com, sep-ass, split-union, |
| true-emp | proved | all subs proved | sep-com, sep-ass, emp-sep, true-elim, true-rev, true, |
| true-and | proved | all subs proved | and-com, and-ass, prop, and, true, |
| stability | proved | all subs proved | septract, split-union, sep-com, this, sep, Imp, |
| precise-disj | proved | all subs proved | precise, trueH, precise-same, true-elim, sep-com, sep-ass, sep, |
| imp-mono | proved | all subs proved | sep-com, sep-ass, split-union, sep, |
| false-and | proved | all subs proved | and-com, and-ass, prop, and, false, |
| eq-frame | proved | all subs proved | sep-com, sep-ass, emp-sep, |
| and-weaken-this | proved | all subs proved | imp, and-com, and-ass, and, |
| and-weaken | proved | all subs proved | and-com, and-ass, and, imp, |
| adjunction | proved | all subs proved | sep-com, sep-ass, split-union, wand, sep, imp, |
| Imp2 | proved | all subs proved | sep-com, sep-ass, split-union, sep, Imp, |
| Imp-frame | proved | all subs proved | sep-com, sep-ass, emp-sep, Imp, |
| Frame | proved | all subs proved | sep-com, sep-ass, split-union, wand, Imp, |
| Eq-P | proved | all subs proved | sep-ass, emp-sep, sep-com, |
| true-elim | proved | all subs proved | prop, split-union, sep, true, |
| and-com | proved | all subs proved | and-ass, and, |
| sep-com | proved | all subs proved | split-union, sep, |
| sep-ass | proved | all subs proved | split-union, sep, |
| imp-propfalse | proved | all subs proved | trueH, prop, imp, false, |
| imp-proptrue | proved | all subs proved | trueH, imp, |
| introduce-sharing | proved | all subs proved | sep, wand, this, split-union, sharing, |
| or-com | proved | all subs proved | or-ass, or, |
| precise-sep | proved | all subs proved | precise-same, sep, precise, |
| true-elims | proved | all subs proved | trueH, sharing, |
| wand-same-emp-p | proved | all subs proved | wand-same-emp, sep, |
| or-ass | proved | all subs proved | or, |
| precise-same | proved | all subs proved | precise, |
| and-ass | proved | all subs proved | and, |
| split-union | proved | all subs proved | sep, |
| trueH | proved | all subs proved | prop, true, |
| emp-sep | proved | all subs proved | emp, sep, |
| true-rev | proved | all subs proved | true, |
| wand-same-emp | proved | all subs proved | wand, |
| wand-shift | proved | all subs proved | wand, sep, |
| wand-dual | proved | all subs proved | wand, septract, not, |
| this-emp | proved | all subs proved | emp, this, |
| sharing-emp | proved | all subs proved | emp, sharing, |
| sharing-com | proved | all subs proved | sharing, |
| sep-split-interactive | proved | all subs proved | sep, |
| sep-mp | proved | all subs proved | wand, sep, |
| sep-Mp | proved | all subs proved | wand, sep, Imp, |
| precise-this | proved | all subs proved | this, precise, |
| precise-emp | proved | all subs proved | emp, precise, |
| imp-cases | proved | all subs proved | prop, imp, |
| falseH | proved | all subs proved | prop, false, |
| false-sep | proved | all subs proved | sep, prop, false, |
| false-rev | proved | all subs proved | false, |
| Imp1 | proved | all subs proved | Imp, |
| Imp-trans | proved | all subs proved | Imp, |
| Imp-refl | proved | all subs proved | Imp, |
| Imp-from-eq | proved | all subs proved | Imp, |
| not | axiom | ||
| true | axiom | ||
| septract | axiom | ||
| precise | axiom | ||
| or | axiom | ||
| sharing | axiom | ||
| this | axiom | ||
| false | axiom | ||
| prop | axiom | ||
| emp | axiom | ||
| and | axiom | ||
| imp | axiom | ||
| sep | axiom | ||
| Imp | axiom | ||
| wand | axiom |