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: |
|---|
| subset-uni | proved | all subs proved
| disj-r,
subset,
disj,
subset-at,
diff-at,
at-uni,
diff-in,
in-uni,
subset-in,
ext,
uni-com,
|
| uni-ass | proved | all subs proved
| disj-r,
at-uni,
disj-distr-uni,
disj-com-rw,
disj-distr-uni-com,
in-uni,
ext,
|
| uni-emp-l | proved | all subs proved
| uni-emp,
disj-emp-r,
uni-com,
|
| write-left | proved | all subs proved
| uni-write,
disj-com-rw,
nonnull,
disj-r,
in-write,
disj,
uni-com,
|
| disj-distr-uni-com | proved | all subs proved
| disj-distr-uni,
disj-com,
|
| uni-com | proved | all subs proved
| disj-r,
disj-l,
at-uni,
disj-com-rw,
in-uni,
ext,
|
| uni-inj | proved | all subs proved
| disj-r,
disj-l,
at-uni,
in-uni,
ext,
|
| union-left-singleton-at | proved | all subs proved
| at-write,
disj-singleton-write,
in-alloc,
in-emp,
in-write,
in-uni,
at-uni,
|
| del-uni | proved | all subs proved
| disj-r,
disj-rem,
at-uni,
in-uni,
at-del,
in-del,
ext,
|
| union-left-singleton | proved | all subs proved
| at-del,
at-write,
at-uni,
in-emp,
in-alloc,
in-write,
in-del,
disj-singleton-write,
in-uni,
nonnull,
ext,
|
| disj-distr-uni | proved | all subs proved
| disj-r,
disj-l,
in-uni,
disj,
|
| at-uni | proved | all subs proved
| disj-r,
size-alloc,
size-write,
disj-l,
at-alloc,
in-alloc,
in-write,
disj-write,
at-write,
uni-alloc,
uni-write,
disj-alloc,
sanity,
exin,
ext,
in-emp,
disj-emp-r,
uni-emp,
in-uni,
|
| exin-uni | proved | all subs proved
| in-write,
disj-write,
in-uni,
uni-emp,
uni-alloc,
disj-emp-r,
disj-r,
disj,
in-alloc,
in-emp,
uni-write,
sanity,
exin,
nonnull,
|
| size-uni | proved | all subs proved
| disj-write,
size-alloc,
size-write,
in-alloc,
in-uni,
uni-alloc,
uni-write,
disj-alloc,
sanity,
exin,
in-emp,
ext,
size-emp,
uni-emp,
|
| disj-com | proved | all subs proved
| disj-com-rw,
|
| in-uni | proved | all subs proved
| size-alloc,
size-write,
disj-write,
in-alloc,
in-write,
uni-alloc,
uni-write,
disj-alloc,
sanity,
exin,
ext,
uni-emp,
in-emp,
|
| at-write-mod-three-other | proved | all subs proved
| at-write-mod-two-other,
at-write-other,
|
| diff-size | proved | all subs proved
| in-diffs,
del-notin,
rm-size,
in-del,
diffs-sw,
diffs-ins,
del-new,
write-del,
in-alloc,
size-alloc,
size-write,
sanity,
exin,
diffs-emp,
|
| disj-diff | proved | all subs proved
| diff-in,
disj,
|
| at-write-mod-two-other | proved | all subs proved
| at-write-mod-other,
at-write-other,
|
| rm-size | proved | all subs proved
| size-alloc,
size-write,
in-alloc,
del-new,
write-del,
sanity,
exin,
|
| diff-at | proved | all subs proved
| in-del,
at-del,
size-alloc,
size-write,
in-alloc,
in-write,
diff-alloc,
diff-write,
sanity,
exin,
in-emp,
ext,
diff-emp,
|
| disj-rem | proved | all subs proved
| disj-l,
in-del,
disj,
|
| disj-alloc | proved | all subs proved
| disj-l,
in-alloc,
disj,
|
| disj-write | proved | all subs proved
| nonnull,
disj-l,
in-alloc,
in-write,
disj,
|
| diff-in | proved | all subs proved
| in-del,
size-alloc,
size-write,
in-alloc,
in-write,
diff-alloc,
diff-write,
sanity,
exin,
ext,
diff-emp,
in-emp,
|
| disj-com-rw | proved | all subs proved
| disj-l,
disj,
|
| at-write-mod-three-other-3 | proved | all subs proved
| at-write-mod-two-other-3,
at-write-other,
|
| size-zero | proved | all subs proved
| size-alloc,
size-write,
in-alloc,
sanity,
exin,
in-emp,
ext,
size-emp,
|
| delswr | proved | all subs proved
| diffs-sw,
write-del,
diffs-ins,
|
| structind | proved | all subs proved
| size-alloc,
size-write,
in-alloc,
sanity,
exin,
in-emp,
ext,
|
| at-write-mod-two-other-3 | proved | all subs proved
| at-write-mod-other-2,
at-write-other,
|
| diffs-sw | proved | all subs proved
| at-diffs,
at-del,
in-diffs,
in-del,
ext,
|
| at-write-mod-other | proved | all subs proved
| at-write,
at-write-other,
|
| exin | proved | all subs proved
| at-del,
at-alloc,
at-write,
ext,
in-del,
nonnull,
in-alloc,
in-write,
|
| disj-l | proved | all subs proved
| disj-r,
|
| at-write-mod-three-other-4 | proved | all subs proved
| at-write-mod-two-other-2,
at-write-other,
|
| write-right | proved | all subs proved
| uni-write,
nonnull,
|
| sw-del-add-new | proved | all subs proved
| at-alloc,
at-diffs,
in-alloc,
in-diffs,
at-write,
in-write,
ext,
|
| sw-delswr | proved | all subs proved
| in-del,
sw-delwr,
diffs-ins,
diffs-emp,
|
| diffs-twice | proved | all subs proved
| at-diffs,
in-diffs,
ext,
|
| subset-emp | proved | all subs proved
| ext,
in-emp,
subset,
emp-subset,
|
| sw-del-add-01 | proved | all subs proved
| sw-del-add,
|
| del-notin | proved | all subs proved
| at-del,
in-del,
ext,
|
| subset-in | proved | all subs proved
| subset,
|
| subset-at | proved | all subs proved
| subset,
|
| at-write-mod-two-other-2 | proved | all subs proved
| in-write,
at-write,
|
| disj-emp-r | proved | all subs proved
| in-emp,
disj,
|
| sw-delwr | proved | all subs proved
| at-del,
in-del,
at-write,
in-write,
ext,
|
| write-del | proved | all subs proved
| at-del,
at-write,
in-write,
in-del,
ext,
|
| del-new | proved | all subs proved
| at-alloc,
at-del,
in-alloc,
in-del,
ext,
|
| disj-singleton-write | proved | all subs proved
| in-emp,
in-alloc,
in-write,
disj,
|
| emp-subset | proved | all subs proved
| in-emp,
subset,
|
| in-diffs | proved | all subs proved
| in-del,
diffs-ins,
diffs-emp,
|
| at-diffs | proved | all subs proved
| in-del,
at-del,
diffs-ins,
diffs-emp,
|
| at-write-other | proved | all subs proved
| at-write,
|
| at-write-mod-other-2 | proved | all subs proved
| in-write,
at-write,
|
| sw-del-add | proved | all subs proved
| at-alloc,
at-del,
in-alloc,
in-del,
at-write,
in-write,
ext,
|
| disj-r | proved | all subs proved
| disj,
|
| nonnull | proved | all subs proved
| sanity,
|
| overwrite-split | proved | all subs proved
| at-write,
in-write,
ext,
|
| at-write-same | proved | all subs proved
| at-write,
|
| sw-alloc-put | proved | all subs proved
| at-alloc,
in-alloc,
in-write,
at-write,
ext,
|
| write-again | proved | all subs proved
| at-write,
in-write,
ext,
|
| disj-emp-l | proved | all subs proved
| in-emp,
disj,
|
| del-twice | proved | all subs proved
| at-del,
in-del,
ext,
|
| in-write-strong | proved | all subs proved
| in-write,
|
| overwrite | proved | all subs proved
| at-write,
in-write,
ext,
|
| put-eq | proved | all subs proved
| at-write,
in-write,
ext,
|
| at-write-mod-three-other-2 | proved | all subs proved
| in-write,
at-write,
|
| overwrite-split2 | proved | all subs proved
| at-write,
in-write,
ext,
|
| del-sw | proved | all subs proved
| at-del,
in-del,
ext,
|
| alloc-write | proved | all subs proved
| at-write,
at-alloc,
in-write,
in-alloc,
ext,
|
| sw-put | proved | all subs proved
| at-write,
in-write,
ext,
|
| size-emp | axiom | | |
| uni-emp | axiom | | |
| uni-alloc | axiom | | |
| subset | axiom | | |
| in-emp | axiom | | |
| diff-emp | axiom | | |
| sanity | axiom | | |
| diff-write | axiom | | |
| diff-alloc | axiom | | |
| size-write | axiom | | |
| size-alloc | axiom | | |
| diffs-emp | axiom | | |
| diffs-ins | axiom | | |
| uni-write | axiom | | |
| disj | axiom | | |
| in-del | axiom | | |
| at-del | axiom | | |
| in-alloc | axiom | | |
| at-alloc | axiom | | |
| ext | axiom | | |
| in-write | axiom | | |
| at-write | axiom | | |