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: |
|---|
| theorem | proved | all subs proved
| theoremx,
tolist-size,
solix-to-solitaire,
|
| theoremx | proved | all subs proved
| ordered-precedes,
orderedl-at,
inv-base,
orderedl-base,
solixh-ordered,
covers-ascsubseq,
covers-empty,
solixh-covers,
theoremx-atmost-h,
maxincseqno-def,
theoremx-atleast,
solix-def,
|
| theoremx-atleast | proved | all subs proved
| inv-last-nonempty,
theoremx-atleast-ind,
ascsubseq-base,
inv-base,
precedesex-base,
solix-def,
solix-inv,
precedesex-solix,
|
| precedesex-solix | proved | all subs proved
| precedesex-base,
inv-base,
precedesex-solixh,
solix-def,
|
| solix-inv | proved | all subs proved
| inv-base,
solixh-inv,
solix-def,
|
| solix-to-solitaire | proved | all subs proved
| tolistl-base,
inv-base,
solixh-to-solitaireh,
solix-def,
solitaire-def,
|
| solix-ordered | proved | all subs proved
| inv-base,
orderedl-base,
solixh-ordered,
solix-def,
|
| theoremx-atmost-h | proved | all subs proved
| coversi-append,
ascsubseq-single,
ascsubseq-nodups,
covers-rem,
ascsubseq-rem,
precedes-ascsubseq-2,
coversi-empty,
|
| solixh-to-solitaireh | proved | all subs proved
| pushx-inv,
pushx-cut-seq,
pushix-to-push,
solixh-rec,
solitaireh-rec,
solixh-base,
solitaireh-base,
|
| solixh-ordered | proved | all subs proved
| pushx-ordered,
pushx-inv-gen,
solixh-rec,
solixh-base,
|
| solixh-inv | proved | all subs proved
| pushx-inv-gen,
solixh-rec,
solixh-base,
|
| precedesex-solixh | proved | all subs proved
| pushx-inv-gen,
precedesex-pushix,
solixh-rec,
solixh-base,
|
| solix-covers | proved | all subs proved
| covers-def,
solixh-covers,
solix-def,
|
| precedes-ascsubseq-2 | proved | all subs proved
| precedes-ascsubseq-2-h,
|
| ascsubseq-nodups | proved | all subs proved
| precedes-trans,
ascsubseq-rest-notprec-first,
ascsubseq-rec,
ascsubseq-first-notin-rest,
|
| theoremx-atleast-ind | proved | all subs proved
| ascsubseq-append,
inv-butlast,
precedesex-rev-rec1,
allls-in,
inv-single,
ascsubseq-single,
precedesex-rec0,
|
| pushix-to-push | proved | all subs proved
| tolistl-cut-seq,
tolist-cut-seq,
allls-rec,
tolist-rec,
push-rec,
pushx-rec,
inv-rec,
tolistl-rec,
tolist-single,
tolistl-single,
pushx-base,
push-base,
tolistl-base,
|
| pushx-inv | proved | all subs proved
| allls-incbound,
inv-incbound,
allls-rec,
pushx-rec,
inv-rec,
allls-single,
inv-single,
pushx-base,
inv-base,
|
| solixh-covers | proved | all subs proved
| pushx-covers,
solixh-rec,
solixh-base,
|
| pushx-inv-gen | proved | all subs proved
| inv-incbound,
allls-incbound,
allls-rec,
pushx-rec,
inv-rec,
allls-single,
inv-single,
pushx-base,
inv-base,
|
| ascsubseq-rem | proved | all subs proved
| precedes-def,
ascsubseq-base,
ascsubseq-single,
ascsubseq-rec,
ascsubseq-prepend,
|
| precedesex-rev-rec1 | proved | all subs proved
| precedesex-rec1,
precedesex-prepend,
precedesex-rec0,
precedesex-2,
|
| ascsubseq-append | proved | all subs proved
| ascsubseq-single,
ascsubseq-rec,
ascsubseq-2,
|
| covers-ascsubseq | proved | all subs proved
| ascsubseq-in-size,
coversi-def,
covers-def,
|
| ordered-precedes | proved | all subs proved
| precedes-def,
ordered-precedes-h,
precedes-notsame,
|
| pushx-ordered | proved | all subs proved
| ordered-rec2,
allls-rec,
pushx-rec,
orderedl-rec,
inv-rec,
ordered-rec1,
ordered-single,
pushx-base,
orderedl-base,
inv-base,
|
| pushx-covers | proved | all subs proved
| covers-def,
pushx-nonrec,
|
| inv-incbound | proved | all subs proved
| allls-incbound,
inv-rec,
inv-base,
|
| tolistl-cut-seq | proved | all subs proved
| tolist-cut-seq,
inv-rec,
tolistl-rec,
tolistl-base,
|
| precedesex-pushix | proved | all subs proved
| precedes-def,
precedesex-2,
precedesex-rec1,
precedesex-prepend,
allls-rec,
pushx-rec,
inv-rec,
precedesex-rec0,
pushx-base,
precedesex-base,
inv-base,
|
| precedes-ascsubseq-2-h | proved | all subs proved
| precedes-trans,
ascsubseq-rec,
|
| ascsubseq-first-notin-rest | proved | all subs proved
| precedes-trans,
precedes-irrefl,
precedes-notsame,
ascsubseq-rec,
ascsubseq-single,
|
| ascsubseq-rest-notprec-first | proved | all subs proved
| precedes-trans,
precedes-irrefl,
ascsubseq-rec,
ascsubseq-single,
|
| precedesex-append | proved | all subs proved
| precedes-append,
precedesex-rec1,
precedesex-rec0,
inv-rec,
precedesex-base,
inv-base,
|
| coversi-empty | proved | all subs proved
| coversi-def,
|
| covers-rem | proved | all subs proved
| coversi-def,
|
| coversi-append | proved | all subs proved
| coversi-def,
|
| allls-in | proved | all subs proved
| allls-rec,
|
| inv-butlast | proved | all subs proved
| inv-rec,
inv-base,
|
| inv-last-nonempty | proved | all subs proved
| inv-rec,
|
| covers-empty | proved | all subs proved
| covers-def,
|
| orderedl-at | proved | all subs proved
| orderedl-base,
orderedl-rec,
|
| tolist-size | proved | all subs proved
| tolistl-rec,
tolistl-base,
|
| pushx-cut-seq | proved | all subs proved
| allls-rec,
pushx-rec,
inv-rec,
pushx-base,
|
| ordered-single | proved | all subs proved
| orderedl-base,
orderedl-rec,
|
| inv-single | proved | all subs proved
| inv-base,
inv-rec,
|
| allls-single | proved | all subs proved
| allls-base,
allls-rec,
|
| pushx-nonrec | proved | all subs proved
| pushx-rec,
pushx-base,
|
| tolistl-single | proved | all subs proved
| tolistl-base,
tolistl-rec,
|
| tolist-single | proved | all subs proved
| tolist-base-02,
tolist-rec,
|
| tolist-cut-seq | proved | all subs proved
| allls-rec,
tolist-rec,
tolist-base-02,
|
| precedesex-prepend | proved | all subs proved
| precedesex-rec1,
precedesex-base,
precedesex-rec0,
|
| precedesex-2 | proved | all subs proved
| precedesex-rec0,
precedesex-rec1,
|
| precedes-append | proved | all subs proved
| precedes-def,
|
| ordered-precedes-h | proved | all subs proved
| ordered-rec2,
|
| allls-incbound | proved | all subs proved
| allls-rec,
allls-base,
|
| ascsubseq-in-size | proved | all subs proved
| precedes-def,
ascsubseq-rec,
ascsubseq-single,
|
| ascsubseq-prepend | proved | all subs proved
| ascsubseq-rec,
ascsubseq-base,
ascsubseq-single,
|
| precedes-notsame | proved | all subs proved
| precedes-def,
|
| precedes-irrefl | proved | all subs proved
| precedes-def,
|
| precedes-trans | proved | all subs proved
| precedes-def,
|
| ascsubseq-2 | proved | all subs proved
| precedes-def,
ascsubseq-single,
ascsubseq-rec,
|
| ascsubseq-empty | proved | all subs proved
| ascsubseq-rec,
ascsubseq-single,
ascsubseq-base,
|
| tolist-base-02 | axiom | | |
| maxincseqno-def | axiom | | |
| solitaireh-base | axiom | | |
| solitaireh-rec | axiom | | |
| solitaire-def | axiom | | |
| ordered-rec1 | axiom | | |
| tolistl-base | axiom | | |
| push-base | axiom | | |
| tolistl-rec | axiom | | |
| push-rec | axiom | | |
| tolist-rec | axiom | | |
| solixh-base | axiom | | |
| solixh-rec | axiom | | |
| solix-def | axiom | | |
| pushx-base | axiom | | |
| pushx-rec | axiom | | |
| precedesex-base | axiom | | |
| precedesex-rec1 | axiom | | |
| precedesex-rec0 | axiom | | |
| orderedl-rec | axiom | | |
| orderedl-base | axiom | | |
| ordered-rec2 | axiom | | |
| inv-base | axiom | | |
| inv-rec | axiom | | |
| covers-def | axiom | | |
| coversi-def | axiom | | |
| ascsubseq-base | axiom | | |
| ascsubseq-rec | axiom | | |
| ascsubseq-single | axiom | | |
| precedes-def | axiom | | |
| allls-base | axiom | | |
| allls-rec | axiom | | |