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: |
|---|
| neg-14 | proved | all subs proved
| neg-zero,
add-comm,
add-assoc,
zero-07,
negeq,
|
| neg-zero | proved | all subs proved
| neg-10,
add-comm,
add-assoc,
sub-eq-01,
neg,
|
| eqint-sub | proved | all subs proved
| eqint-neg,
eqint-add,
|
| mone-02 | proved | all subs proved
| add-comm,
add-assoc,
mone,
|
| neg-02 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
negr-ls,
|
| neg-eq | proved | all subs proved
| double-neg,
|
| neg-10 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
negeq,
|
| double-neg | proved | all subs proved
| add-comm,
add-assoc,
sub-eq-01,
negeq,
|
| negr-ls | proved | all subs proved
| negl-ls,
negeq,
irref,
plst,
ls-num,
bls-01,
l,
add-comm,
add-assoc,
sub-eq-01,
|
| mone | proved | all subs proved
| negeq,
add-comm,
add-assoc,
sub-eq-01,
add-in,
|
| eqint-neg | proved | all subs proved
| eqint-num,
add-comm,
add-assoc,
sub-eq-01,
eqint-add,
negeq,
|
| mone-01 | proved | all subs proved
| negeq,
add-comm,
|
| neg-12 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
sub-eq,
negeq,
|
| rew-eqzero | proved | all subs proved
| negeq,
add-comm,
|
| rew-eqzero-01 | proved | all subs proved
| negeq,
|
| negeq | proved | all subs proved
| add-in,
add-comm,
add-assoc,
sub-eq-01,
|
| eqnum-add1 | proved | all subs proved
| add-comm,
add-assoc,
add-in,
eqint-add,
|
| eqnum-addboth1 | proved | all subs proved
| add-comm,
add-assoc,
add-in,
eqint-add,
|
| eqnum-addboth2 | proved | all subs proved
| add-comm,
add-assoc,
add-in,
eqint-add,
|
| lst-05 | proved | all subs proved
| not-zero-pos,
irref,
bls-01,
add-comm,
add-assoc,
add-less,
trans,
ls,
less-add-cancel-l,
eq,
add-in,
ls-02,
ex-ls-add,
add-zero,
pls,
l,
|
| neg-add | proved | all subs proved
| add-assoc,
add-comm,
add-zero,
sub-eq-01,
add-in,
|
| zero-07 | proved | all subs proved
| not-zero-pos,
zero,
blst-01,
add-comm,
add-assoc,
add-zero,
|
| add-in | proved | all subs proved
| bls-01,
add-comm,
add-assoc,
irref,
less-add-cancel-l,
blst-01,
|
| lsls-add-notgr | proved | all subs proved
| add-comm,
add-assoc,
less-add-cancel-l,
bls-01,
trans-lem,
|
| lst | proved | all subs proved
| add-comm,
add-assoc,
lst-04,
|
| lst-02 | proved | all subs proved
| bls-01,
add-comm,
add-assoc,
less-add-cancel-l,
trans,
l,
neq-01,
|
| pls-03 | proved | all subs proved
| add-comm,
add-assoc,
nls,
|
| pls-04 | proved | all subs proved
| add-comm,
add-assoc,
nls,
|
| plst-01 | proved | all subs proved
| lst-04,
trans,
add-comm,
add-assoc,
irref,
less-add-cancel-l,
bls-01,
l,
|
| ttwo | proved | all subs proved
| forward-any-lsle,
less-add-cancel-l,
trans,
add-comm,
add-assoc,
nls,
|
| zero-03 | proved | all subs proved
| bls-01,
add-comm,
add-assoc,
ls,
trans,
l,
zero-05,
|
| zero-05 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
blst-02,
not-zero-pos,
|
| nls | proved | all subs proved
| forward-any-lsle,
irref,
add-comm,
add-assoc,
less-add-cancel-l,
blst-02,
pls,
|
| plst | proved | all subs proved
| forward-any-lsle,
add-assoc,
less-add-cancel-l,
irref,
add-comm,
pls,
bls-01,
blst-02,
|
| ex-ls-add | proved | all subs proved
| neg-09,
add-zero,
sub-eq-01,
add-comm,
add-assoc,
add-less,
|
| neq-01 | proved | all subs proved
| forward-any-lsle,
add-comm,
add-assoc,
less-add-cancel-l,
|
| lst-04 | proved | all subs proved
| add-comm,
add-assoc,
bls-01,
less-add-cancel-l,
forward-any-lsle,
|
| trans-lem | proved | all subs proved
| forward-any-lsle,
trans,
|
| blst-01 | proved | all subs proved
| blst-02,
|
| blst | proved | all subs proved
| forward-any-lsle,
trans,
|
| forward-pos | proved | all subs proved
| forward-any-lsle,
trans,
|
| lf-02 | proved | all subs proved
| forward-any-lsle,
|
| lf-03 | proved | all subs proved
| forward-any-lsle,
|
| lf-04 | proved | all subs proved
| forward-any-lsle,
lf-08,
|
| lf-05 | proved | all subs proved
| forward-any-lsle,
|
| lf-06 | proved | all subs proved
| forward-any-lsle,
|
| lsnum-add3 | proved | all subs proved
| add-comm,
add-assoc,
add-less,
ls-02,
eqint-add,
|
| lst-03 | proved | all subs proved
| forward-any-lsle,
add-comm,
add-assoc,
less-add-cancel-l,
|
| trans-lem3 | proved | all subs proved
| forward-any-lsle,
lf-08,
|
| add-less | proved | all subs proved
| irref,
add-comm,
add-assoc,
bls-01,
ls,
eq,
l,
|
| blst-02 | proved | all subs proved
| l,
irref,
|
| forward-any-lsle | proved | all subs proved
| lf-07,
lf-08,
|
| lst-01 | proved | all subs proved
| add-comm,
add-assoc,
bls-01,
less-add-cancel-l,
trans,
l,
|
| mone-03 | proved | all subs proved
| ls-num,
add-zero,
less-add-cancel-l,
eqint-num,
add-comm,
add-assoc,
eqint-add,
l,
|
| neg-01 | proved | all subs proved
| add-comm,
add-assoc,
neg-09,
negl-ls,
|
| neq | proved | all subs proved
| add-comm,
add-assoc,
bls-01,
l,
ls,
|
| pls-01 | proved | all subs proved
| ls,
trans,
bls-01,
add-comm,
add-assoc,
add-zero,
l,
|
| pls-02 | proved | all subs proved
| trans,
bls-01,
add-comm,
add-assoc,
ls,
l,
|
| zero-01 | proved | all subs proved
| add-comm,
add-assoc,
ls-zero,
zero,
l,
|
| zero-02 | proved | all subs proved
| add-comm,
add-assoc,
bls-01,
ls,
trans,
not-zero-pos,
l,
|
| zero-06 | proved | all subs proved
| not-zero-pos,
l,
add-comm,
add-assoc,
add-zero,
|
| lf-07 | proved | all subs proved
| lf-08,
|
| neg-09 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
negradd-ls,
|
| l | proved | all subs proved
| total,
irref,
lf-08,
bls-01,
|
| eqnum-add2 | proved | all subs proved
| add-comm,
add-assoc,
eq,
eqint-add,
|
| neg-05 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
negl-ls,
|
| neg-08 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
negladd-ls,
|
| negadd | proved | all subs proved
| add-comm,
add-assoc,
negradd-ls,
negladd-ls,
|
| negadd-eq | proved | all subs proved
| add-assoc,
add-comm,
add-zero,
sub-eq-01,
sub-eq,
|
| sub-ls-02 | proved | all subs proved
| add-comm,
add-assoc,
negladd-ls,
|
| zero | proved | all subs proved
| irref,
trans,
add-comm,
add-assoc,
add-zero,
pls,
|
| ls-zero | proved | all subs proved
| add-comm,
add-assoc,
bls-01,
ls-02,
trans,
|
| sub-eq | proved | all subs proved
| add-assoc,
add-comm,
add-zero,
sub-eq-01,
|
| negradd-ls | proved | all subs proved
| add-assoc,
add-comm,
add-zero,
sub-eq-01,
less-add-cancel-l,
|
| negladd-ls | proved | all subs proved
| add-assoc,
add-comm,
add-zero,
sub-eq-01,
less-add-cancel-l,
|
| negl-ls | proved | all subs proved
| add-comm,
add-assoc,
sub-eq-01,
less-add-cancel-l,
|
| not-zero-pos | proved | all subs proved
| irref,
add-comm,
add-assoc,
ls-02,
add-zero,
trans,
less-add-cancel-l,
|
| lf-08 | proved | all subs proved
| trans,
bls-01,
total,
|
| eq | proved | all subs proved
| sub-eq-01,
add-comm,
add-assoc,
add-zero,
|
| inv-add | proved | all subs proved
| add-comm,
add-assoc,
sub-eq-01,
|
| ls-03 | proved | all subs proved
| add-comm,
add-assoc,
ls,
|
| lsls-add-noteq | proved | all subs proved
| add-comm,
add-assoc,
irref,
less-add-cancel-l,
pls,
|
| lsnum-add2 | proved | all subs proved
| add-comm,
add-assoc,
ls,
eqint-add,
|
| pls | proved | all subs proved
| add-assoc,
trans,
add-comm,
less-add-cancel-l,
|
| ls-02 | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
less-add-cancel-l,
|
| sub-eq-01 | proved | all subs proved
| add-comm,
add-assoc,
neg,
|
| ls | proved | all subs proved
| add-comm,
add-assoc,
add-zero,
less-add-cancel-l,
|
| bls-01 | proved | all subs proved
| irref,
trans,
|
| betweenlsls-zero-one | proved | all subs proved
| ls-num,
|
| ex-oddeven | proved | all subs proved
| add-comm,
add-assoc,
|
| lsnum-add1 | proved | all subs proved
| add-comm,
add-assoc,
less-add-cancel-l,
eqint-add,
|
| lsnum-add4 | proved | all subs proved
| add-comm,
add-assoc,
less-add-cancel-l,
eqint-add,
|
| lsnum-addboth1 | proved | all subs proved
| add-comm,
add-assoc,
less-add-cancel-l,
eqint-add,
|
| lsnum-addboth2 | proved | all subs proved
| add-comm,
add-assoc,
less-add-cancel-l,
eqint-add,
|
| trans-lem2 | proved | all subs proved
| trans,
|
| neg | axiom | | |
| total | axiom | | |
| eqint-add | axiom | | |
| eqint-num | axiom | | |
| add-zero | axiom | | |
| trans | axiom | | |
| ls-num | axiom | | |
| less-add-cancel-l | axiom | | |
| irref | axiom | | |
| add-assoc | axiom | | |
| add-comm | axiom | | |