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: |
|---|
| Data-notin-other-3 | proved | all subs proved
| Data-notin-other,
Data-notin-other-2,
|
| Data-notin-other-2 | proved | all subs proved
| Data-notin-other,
|
| Data-notin-other | proved | all subs proved
| In-data-in,
in-neq,
At-same,
At-other,
Data-in,
|
| Data-in-putdelput | proved | all subs proved
| In-data-in,
Del-at,
Del-in,
in-neq,
At-other,
At-same,
Data-in,
|
| Data-in-putdel | proved | all subs proved
| In-data-in,
Del-at,
Del-in,
in-neq,
At-other,
At-same,
Data-in,
|
| Data-in-delput-2 | proved | all subs proved
| In-data-in,
in-neq,
At-other,
At-same,
Del-at,
Del-in,
Data-in,
|
| Data-in-delput | proved | all subs proved
| In-data-in,
in-neq,
At-other,
At-same,
Del-at,
Del-in,
Data-in,
|
| Data-in-del | proved | all subs proved
| In-data-in,
Del-at,
Del-in,
Data-in,
|
| In-data-in | proved | all subs proved
| Data-in-putsame,
At-same,
exin,
|
| inex | proved | all subs proved
| At-same,
In-insert,
exin,
Extension,
|
| exputin | proved | all subs proved
| put-neq-01,
In-insert,
exin,
|
| exin | proved | all subs proved
| In-insert,
del-exists,
|
| sw-01 | proved | all subs proved
| Del-in,
deldel,
lookupisempty,
Del-at,
Extension,
|
| deldel | proved | all subs proved
| lookupisempty,
Del-in,
del-notin,
Del-at,
Extension,
|
| del-exists | proved | all subs proved
| rew,
insins,
In-insert,
At-same,
At-other,
In-empty,
|
| sw | proved | all subs proved
| delete-put-rew,
|
| subset-put-strong-02 | proved | all subs proved
| subset-put-strong-05,
|
| subset-put-strong-01 | proved | all subs proved
| subset-put-strong-04,
|
| subset-put-strong | proved | all subs proved
| subset-put-strong-03,
|
| empty | proved | all subs proved
| In-insert,
At-same,
Size-empty,
notmemlookup,
Del-in,
del-put,
Size-insert,
indef,
In-empty,
Extension,
|
| dom-isemp | proved | all subs proved
| dom-ins,
exnotempty,
dom-emp,
|
| del-empty | proved | all subs proved
| In-empty,
del-notin,
|
| delete-put-rew | proved | all subs proved
| lookupisempty,
At-other,
in-neq,
In-insert,
Del-at,
At-same,
Del-in,
Extension,
|
| subset-put-strong-05 | proved | all subs proved
| subset-elem-eq-02,
At-other,
At-same,
superset-elem-in-01,
in-neq,
In-insert,
Subset,
|
| subset-put-strong-04 | proved | all subs proved
| subset-elem-eq-02,
At-other,
At-same,
superset-elem-in-01,
in-neq,
In-insert,
Subset,
|
| subset-put-strong-03 | proved | all subs proved
| subset-elem-eq-02,
At-other,
At-same,
superset-elem-in-01,
in-neq,
In-insert,
Subset,
|
| indef | proved | all subs proved
| At-other,
in-neq,
At-same,
In-insert,
Extension,
del-put,
|
| exnotempty | proved | all subs proved
| Del-in,
ins-same,
del-put,
notmemlookup,
In-empty,
Extension,
neq,
|
| rew | proved | all subs proved
| In-insert,
At-other,
At-same,
in-neq,
k-Extension,
|
| del-notin | proved | all subs proved
| Del-at,
Del-in,
k-Extension,
|
| subset-put-01 | proved | all subs proved
| At-other,
ins-same,
In-insert,
Subset,
|
| subset-put | proved | all subs proved
| At-other,
ins-same,
In-insert,
Subset,
|
| put-same | proved | all subs proved
| Extension,
insins,
|
| insert | proved | all subs proved
| At-other,
in-neq,
Del-in,
lookupisempty,
Del-at,
Extension,
|
| ins-same-01 | proved | all subs proved
| In-insert,
ins-same,
Extension,
|
| inj-put-01 | proved | all subs proved
| put-neq,
|
| inj-put | proved | all subs proved
| ins,
At-same,
At-other,
In-insert,
ins-same,
Extension,
|
| eq-shift-put | proved | all subs proved
| At-other,
in-neq,
Extension,
In-insert,
At-same,
ins-same,
insins,
|
| del-putsame | proved | all subs proved
| At-other,
in-neq,
At-same,
In-insert,
Extension,
del-put,
|
| subset-elem-eq-02 | proved | all subs proved
| subset-elem-eq-01,
|
| put-neq | proved | all subs proved
| notmemlookup,
In-insert,
At-same,
At-other,
Extension,
|
| ins | proved | all subs proved
| At-other,
in-neq,
At-same,
In-insert,
Extension,
|
| ins-same | proved | all subs proved
| At-other,
in-neq,
At-same,
In-insert,
Extension,
|
| lookupisempty | proved | all subs proved
| Del-in,
notmemlookup,
|
| del-put | proved | all subs proved
| Del-at,
At-other,
in-neq,
Del-in,
In-insert,
At-same,
Extension,
|
| k-Extension | proved | all subs proved
| notmemlookup,
Extension,
|
| insins | proved | all subs proved
| At-other,
in-neq,
In-insert,
At-same,
Extension,
|
| superset-elem-eq | proved | all subs proved
| subset-elem-eq-01,
|
| subset-empty-01 | proved | all subs proved
| notmemlookup,
Extension,
In-empty,
Subset,
|
| subset-delete | proved | all subs proved
| subset-delete-01,
|
| ins3 | proved | all subs proved
| At-other,
in-neq,
In-insert,
At-same,
Extension,
|
| indef-01 | proved | all subs proved
| At-other,
in-neq,
At-same,
In-insert,
Extension,
|
| Data-in-puteq | proved | all subs proved
| Data-in-putsame,
|
| superset-elem-in-01 | proved | all subs proved
| Subset,
|
| subset-elem-eq-01 | proved | all subs proved
| Subset,
|
| subset-delete-01 | proved | all subs proved
| Del-at,
Del-in,
Subset,
|
| put-neq-01 | proved | all subs proved
| At-same,
Extension,
|
| neq | proved | all subs proved
| In-insert,
At-same,
In-empty,
Extension,
|
| notmemlookup | proved | all subs proved
| At-other,
In-insert,
|
| dom-emp | proved | all subs proved
| In-empty,
Dom,
|
| dom-ins | proved | all subs proved
| In-insert,
Dom,
|
| Data-in-putsame | proved | all subs proved
| In-insert,
At-same,
Data-in,
|
| in-neq | proved | all subs proved
| In-insert,
|
| superset-elem-in | proved | all subs proved
| Subset,
|
| subset-empty | proved | all subs proved
| In-empty,
Subset,
|
| subset-elem-eq | proved | all subs proved
| Subset,
|
| subset-delete-02 | proved | all subs proved
| Del-at,
Del-in,
Subset,
|
| sub-trans | proved | all subs proved
| Subset,
|
| sub-ref | proved | all subs proved
| Subset,
|
| notin-emp | proved | all subs proved
| In-empty,
Extension,
|
| insin | proved | all subs proved
| In-insert,
|
| in-notemp | proved | all subs proved
| In-empty,
|
| dom-del | proved | all subs proved
| Del-in,
Dom,
|
| At-other-strong | proved | all subs proved
| At-other,
|
| At-other-num | proved | all subs proved
| At-other,
|
| At-in-out | proved | all subs proved
| At-other,
At-same,
|
| Subset | axiom | | |
| Size-insert | axiom | | |
| Size-empty | axiom | | |
| Dom | axiom | | |
| Extension | axiom | | |
| In-empty | axiom | | |
| In-insert | axiom | | |
| Data-in | axiom | | |
| Del-in | axiom | | |
| Del-at | axiom | | |
| At-same | axiom | | |
| At-other | axiom | | |