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: |
|---|
| bmin-two-06 | proved | all subs proved
| bmin-two-07,
min-inn,
|
| bmin-sub-01 | proved | all subs proved
| bmin-two-01,
min-one,
bmin-two-02,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
size-two,
min-sub,
bmin-two-07,
min-subset,
|
| bmin-two-07 | proved | all subs proved
| bmin-two-01,
bmin-two-02,
size-two,
|
| bmin-two-08 | proved | all subs proved
| min-two,
bmin-two-01,
min-two-01,
min-one,
bmin-two-02,
size-two,
|
| bmin-two-05 | proved | all subs proved
| bmin-two-01,
min-two,
min-one,
bmin-two-02,
min-two-01,
size-two,
|
| bmin-two-04 | proved | all subs proved
| bmin-two-01,
min-two,
min-one,
bmin-two-02,
min-two-01,
size-two,
|
| bmin-two | proved | all subs proved
| bmin-two-01,
min-one,
bmin-two-02,
size-two,
|
| bmin-sub-02 | proved | all subs proved
| bmin-two-01,
min-two,
min-one,
bmin-two-02,
min-two-01,
size-two,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
|
| bmin-two-02 | proved | all subs proved
| bmin-two-01,
|
| minmax-01 | proved | all subs proved
| Min-min,
Max-max,
min-one-01,
Min-in,
Max-in,
Butmin,
|
| minmax | proved | all subs proved
| max-one-01,
min-one-01,
Min-in,
Max-in,
Butmax,
Butmin,
|
| min-two-02 | proved | all subs proved
| min-two,
min-two-01,
max-one,
max-ifins,
minmax-04,
Min-in,
Max-in,
min-less,
Min-min,
Max-max,
|
| min-ins-02 | proved | all subs proved
| min-ins-03,
min-insert,
min-q,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| max-ins-01 | proved | all subs proved
| max-ifins,
|
| max-ins | proved | all subs proved
| max-ifins,
|
| bmin-two-03 | proved | all subs proved
| min-two,
bmin-two-01,
|
| bmin-one-03 | proved | all subs proved
| min-one-01,
Butmin,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| bmin-nin-02 | proved | all subs proved
| bmin-in-02,
|
| bmin-del-04 | proved | all subs proved
| min-del-01,
bmin-del-05,
bmin-del-02,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-del-03 | proved | all subs proved
| bmin-del-02,
min-del-01,
Butmin,
|
| bmin-bls | proved | all subs proved
| min-one-01,
min-delmin,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmax-one-01 | proved | all subs proved
| max-one-01,
Butmax,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| min-ins-03 | proved | all subs proved
| min-insert,
min-ins-01,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| max-ifins | proved | all subs proved
| max-gr,
max-q,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
max-one,
|
| min-two-01 | proved | all subs proved
| min-two,
|
| bmin-two-01 | proved | all subs proved
| min-two,
bmin-del-05,
|
| bmin-in-02 | proved | all subs proved
| bmin-in,
|
| min-del-01 | proved | all subs proved
| min-del,
|
| min-one-01 | proved | all subs proved
| min-one,
|
| max-one-01 | proved | all subs proved
| max-one,
|
| max-bmin | proved | all subs proved
| minmax-02,
max-del-01,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| butmin-ins | proved | all subs proved
| min-insert,
min-ins-01,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-one | proved | all subs proved
| min-one,
bmin-del-05,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| bmax-shift | proved | all subs proved
| max-del-01,
Butmax,
|
| bmax-one | proved | all subs proved
| max-one,
Butmax,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| bmax-min | proved | all subs proved
| minmax-02,
min-del,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmax,
|
| bm-shift | proved | all subs proved
| bmin-del-02,
min-del,
minmax-02,
max-del-01,
bmax-def,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmax,
Butmin,
|
| min-ins-01 | proved | all subs proved
| min-q,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
|
| min-two | proved | all subs proved
| min-q,
|
| min-one | proved | all subs proved
| min-q,
|
| bmin-in | proved | all subs proved
| min-inn,
Min-min,
Max-max,
ins-inbutmins,
|
| max-one | proved | all subs proved
| max-q,
|
| max-del-01 | proved | all subs proved
| max-gr,
max-in,
max-q,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| minmax-02 | proved | all subs proved
| minmax-03,
max-gr,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| min-del | proved | all subs proved
| min-q,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| min-ins-04 | proved | all subs proved
| min-insert,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| butmin-ins-01 | proved | all subs proved
| min-insert,
Butmin,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| bmin-sub-05 | proved | all subs proved
| min-sub-01,
min-less,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-min | proved | all subs proved
| min-delmin-01,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| minmax-03 | proved | all subs proved
| minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| min-q | proved | all subs proved
| minmax-04,
Min-in,
Max-in,
min-less,
Min-min,
Max-max,
|
| max-q | proved | all subs proved
| max-in,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
|
| min-insert | proved | all subs proved
| min-inn,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| min-sub-01 | proved | all subs proved
| minmax-04,
min-less,
Min-in,
Max-in,
Min-min,
Max-max,
|
| min-delmin-01 | proved | all subs proved
| min-subset,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| ins-inbutmins | proved | all subs proved
| Min-min,
Max-max,
bmin-f,
bmin-in-01,
|
| min-delmin | proved | all subs proved
| min-subset,
min-less,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| maxunion | proved | all subs proved
| max-in,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| max-subset | proved | all subs proved
| minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
|
| ls-rm | proved | all subs proved
| max-in,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
Greater,
|
| ls-add | proved | all subs proved
| max-in,
minmax-04,
Min-in,
Max-in,
Min-min,
Max-max,
Greater,
|
| bminmin | proved | all subs proved
| min-ins-05,
Butmin,
|
| bmin-size | proved | all subs proved
| min-ls,
Butmin,
|
| bmin-in-04 | proved | all subs proved
| min-subset,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-eq | proved | all subs proved
| min-ins-05,
Butmin,
|
| bmin-bneq | proved | all subs proved
| minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-bin | proved | all subs proved
| min-subset,
minmax-04,
Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmax-max | proved | all subs proved
| Min-min,
Max-max,
Min-in,
Max-in,
max-del,
Butmax,
|
| bmin-in-01 | proved | all subs proved
| Butmin,
min-less,
Min-min,
Max-max,
|
| min-ls | proved | all subs proved
| min-inn,
|
| min-ins-05 | proved | all subs proved
| min-inn,
|
| min-subset | proved | all subs proved
| min-sub,
|
| max-del | proved | all subs proved
| max-subset-01,
Max-max,
|
| minmax-04 | proved | all subs proved
| max-gr,
Min-in,
Max-in,
|
| min-ins | proved | all subs proved
| min-inn,
|
| min-inc | proved | all subs proved
| min-inn,
|
| bmin-one-02 | proved | all subs proved
| Min-in,
Max-in,
min-less,
Butmin,
Min-min,
Max-max,
|
| bmin-del-01 | proved | all subs proved
| bmin-del-02,
Butmin,
|
| max-gr | proved | all subs proved
| Min-in,
Max-in,
Min-min,
Max-max,
|
| max-subset-01 | proved | all subs proved
| Min-min,
Max-max,
Min-in,
Max-in,
|
| max-in | proved | all subs proved
| Min-in,
Max-in,
|
| bmin-f | proved | all subs proved
| Butmin,
|
| min-sub | proved | all subs proved
| Min-min,
Max-max,
Min-in,
Max-in,
|
| min-less | proved | all subs proved
| Min-min,
Max-max,
|
| min-inn | proved | all subs proved
| Min-in,
Max-in,
|
| bmin-del-05 | proved | all subs proved
| Butmin,
|
| bmax-def | proved | all subs proved
| Butmax,
|
| bmin-del-02 | proved | all subs proved
| Butmin,
|
| min-intempty | proved | all subs proved
| Min-in,
Max-in,
Min-min,
Max-max,
|
| ls-emptyset | proved | all subs proved
| Greater,
|
| emptyset-ls | proved | all subs proved
| Less,
|
| diff-min | proved | all subs proved
| Min-in,
Max-in,
Min-min,
Max-max,
|
| butminempty-sizeone | proved | all subs proved
| Min-in,
Max-in,
Butmin,
|
| butmin-in | proved | all subs proved
| Butmin,
|
| bmin-sub-04 | proved | all subs proved
| Butmin,
|
| bmin-sub-03 | proved | all subs proved
| Butmin,
|
| bmin-sub | proved | all subs proved
| Butmin,
|
| bmin-size-02 | proved | all subs proved
| Min-in,
Max-in,
Butmin,
|
| bmin-size-01 | proved | all subs proved
| Min-in,
Max-in,
Butmin,
|
| bmin-one-01 | proved | all subs proved
| Min-in,
Max-in,
Butmin,
|
| bmin-nin-01 | proved | all subs proved
| Butmin,
|
| bmin-nin | proved | all subs proved
| Butmin,
|
| bmin-intempty | proved | all subs proved
| Butmin,
|
| bmin-in-03 | proved | all subs proved
| Butmin,
|
| bmin-eq-01 | proved | all subs proved
| Min-min,
Max-max,
Min-in,
Max-in,
Butmin,
|
| bmin-del | proved | all subs proved
| Butmin,
|
| bmax-in-02 | proved | all subs proved
| Butmax,
|
| bmax-in-01 | proved | all subs proved
| Butmax,
|
| bmax-in | proved | all subs proved
| Butmax,
Min-min,
Max-max,
|
| bmax-empty | proved | all subs proved
| Min-in,
Max-in,
Butmax,
|
| Greater | axiom | | |
| Less | axiom | | |
| size-two | proved | all subs proved
| |
| Butmin | axiom | | |
| Butmax | axiom | | |
| Max-in | axiom | | |
| Min-in | axiom | | |
| Max-max | axiom | | |
| Min-min | axiom | | |