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Thin categories, prosets as categories, and poset/toset/lattice #4248

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merged 69 commits into from
Oct 16, 2024
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efc9759
Move moel to main; add ThinCat and indiscrete category
zwang123 Sep 17, 2024
dd59b38
add thincc
zwang123 Sep 17, 2024
ed125d4
Add catcone0 to main; add catprs, prsthinc and related theorems
zwang123 Sep 18, 2024
eacc384
remove ax-un dependency in f1omo
zwang123 Sep 18, 2024
18882e4
remove ax-un for 2oexw and prsthinc
zwang123 Sep 18, 2024
68f32e5
remove ax-un and ax-pow for indthinc
zwang123 Sep 18, 2024
94f7937
shorten 2oexw
zwang123 Sep 18, 2024
a5bf4d0
add mo0sn
zwang123 Sep 19, 2024
58ccf8b
add mofasn2 and related
zwang123 Sep 19, 2024
12c113f
add mofsn3 and rename theorems xxfa* -> xxf*
zwang123 Sep 19, 2024
ae8003f
add setcthin and setc2othin
zwang123 Sep 19, 2024
889d39f
shorten proof by mof02
zwang123 Sep 19, 2024
8ac55a8
rename mofsn3 -> mofmo; and fix description
zwang123 Sep 19, 2024
4f1190f
Add ProsetToCat defining and important properties
zwang123 Sep 20, 2024
38bae43
added two redundant hypotheses to prstchom for explicitness
zwang123 Sep 20, 2024
238382a
add prstchom2ALT
zwang123 Sep 20, 2024
2ed222d
add thincn0eu and prstchom2
zwang123 Sep 20, 2024
0c1f8cd
Resolve merge conflict by incorporating both suggestions
zwang123 Sep 20, 2024
ed5216e
revive ALT theorems
zwang123 Sep 20, 2024
148e9ac
prevent basendx usage
zwang123 Sep 20, 2024
c5f8254
shorten prstchomval
zwang123 Sep 20, 2024
2ee397d
sylibda->sylbida
zwang123 Sep 20, 2024
b9220e6
Add idmon and idepi
zwang123 Sep 21, 2024
80c1fd8
add MndToCat
zwang123 Sep 21, 2024
c9e8378
add grptcmon and grptcepi
zwang123 Sep 22, 2024
3b043e4
add dtrucor3
zwang123 Sep 23, 2024
49325b7
merge develop and resolve conflict
zwang123 Sep 24, 2024
d311b8d
add monepilem, thincid, thincmon, thincepi; shorten grptcmon and grpt…
zwang123 Sep 24, 2024
fc498a5
add mndtcbas2
zwang123 Sep 24, 2024
dda1028
revise mndtcco2; add thinccic and related; add thinccd to shorten proofs
zwang123 Sep 24, 2024
d878d50
move biadanid to main
zwang123 Sep 24, 2024
fd3731d
update changes-set.txt
zwang123 Sep 24, 2024
7d641ec
add postcpos and postc
zwang123 Sep 24, 2024
aee285f
add catmnd
zwang123 Sep 25, 2024
b1cba9a
add theorems from joindm2 to meetdm3; change chapter structure
zwang123 Sep 25, 2024
9119ace
shorten postcpos
zwang123 Sep 26, 2024
a7c67aa
add lubeldm2 and lubsscl and others
zwang123 Sep 26, 2024
5659ae1
add glbpr and lubpr
zwang123 Sep 26, 2024
e3bfc45
split lubpr into 3; same for glbpr; shorten glbpr (now glbprlem)
zwang123 Sep 26, 2024
c075a10
add toslat; move tospos, tleile, tltnle to main
zwang123 Sep 26, 2024
6f289ef
merge and resolve conflict
zwang123 Sep 26, 2024
390b7de
mention setcid and thincid to show how to prove (/) is the identity m…
zwang123 Sep 26, 2024
e1ac292
monepilem -> mpbiran3d; add mpbiran4d
zwang123 Sep 27, 2024
dcd2a97
rename: catmnd -> endmndlem
zwang123 Sep 27, 2024
685c75e
add posjidm and posmidm; fix latjidm and latmidm
zwang123 Sep 27, 2024
19cc828
add ipolubdm and related
zwang123 Sep 28, 2024
3d8d787
prove ipolub
zwang123 Sep 28, 2024
5f24022
prove ipoglb and ipoglbdm
zwang123 Sep 29, 2024
23c8fe3
add oppcthin
zwang123 Sep 29, 2024
5b9cc98
Resolve merge conflict
zwang123 Sep 29, 2024
3467275
fix descriptions
zwang123 Sep 29, 2024
ba21945
add mreclat, mrelatlubALT, and mrelatglbALT
zwang123 Sep 29, 2024
51d15fd
Add topclat
zwang123 Sep 29, 2024
6c480da
Add ipolub00, ipoglb0; toplatlub/toplatglb/toplatglb0
zwang123 Sep 30, 2024
21759cc
add topdlat and related
zwang123 Sep 30, 2024
7780eec
add subthinc
zwang123 Sep 30, 2024
386c83d
Add fullthinc
zwang123 Sep 30, 2024
a1fdf3d
revise fullthinc; add fullthinc2
zwang123 Sep 30, 2024
2b0225f
add thincfth
zwang123 Sep 30, 2024
03deb08
move theorems related to functions to its right place
zwang123 Sep 30, 2024
f228c53
Add functhinc; functhinclem1 -> mofeu
zwang123 Oct 1, 2024
344b2bb
detailed descriptions
zwang123 Oct 1, 2024
96f7ae4
revert: set -> poset
zwang123 Oct 15, 2024
f0e1924
change tleile description based on BJ's suggestion
zwang123 Oct 15, 2024
5e42b6e
change tltnle description based on BJ's suggestion
zwang123 Oct 15, 2024
c4a6d89
change latjidm and latmidm description based on BJ's suggestion
zwang123 Oct 15, 2024
ba9e5cd
revert changes to mreclat.i and rename new mreclat.i to mreclatGOOD.i
zwang123 Oct 15, 2024
d656a1e
Merge branch 'develop' into thin-cat-3
zwang123 Oct 15, 2024
91a6a98
Merge branch 'develop' into thin-cat-3
benjub Oct 16, 2024
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rename mofsn3 -> mofmo; and fix description
zwang123 committed Sep 19, 2024
commit 8ac55a8ac3ca02cc909931dea79ac1a00b755f69
16 changes: 8 additions & 8 deletions set.mm
Original file line number Diff line number Diff line change
@@ -775875,9 +775875,9 @@ additional condition (deduction form). See ~ ralbidc for a more
ZUJUKKUNAUIULJZCTZUKUPUJADCGLMUJUNUPNUKUJUMUOCBUIAULOPQRUJUKUAZKZBSFUNURB
UISUJUQUBUQUISFZUJUQUSDUCUDMUEABCUFUGUH $.

$( At most one function to a implied singleton. ~ mofsn . (Contributed by
Zhi Wang, 19-Sep-2024.) $)
mofsn3 $p |- ( E* x x e. B -> E* f f : A --> B ) $=
$( At most one function to a class containing at most one element.
(Contributed by Zhi Wang, 19-Sep-2024.) $)
mofmo $p |- ( E* x x e. B -> E* f f : A --> B ) $=
( vy cv wcel wmo c0 wceq csn wex wo mo0sn mof02 mofsn2 exlimiv jaoi sylbi
wf ) AFCGAHCIJZCEFZKJZELZMBCDFTDHZAECNUAUEUDBCDOUCUEEBCDUBPQRS $.
$}
@@ -777365,11 +777365,11 @@ separated by (open) neighborhoods. See ~ sepnsepo for the equivalence
(Contributed by Zhi Wang, 20-Sep-2024.) $)
setcthin $p |- ( ph -> C e. ThinCat ) $=
( vy vz vf cfv eqid cv wcel wa wmo mobidv adantr csetc chom setcbas eqidd
cthinc co wf weq elequ2 simprr rspcdva mofsn3 syl simprl elsetchom mpbird
wral ccat setccat isthincd eqeltrd ) ACDUAMZUEGAJKDVBLVBUBMZAVBDEVBNZHUCA
VCUDAJOZDPZKOZDPZQZQZLOZVEVGVCUFPZLRVEVGVKUGZLRZVJFOZVGPZFRZVNVJVOBOPZFRZ
VQBDVGBKUHVRVPFBKFUISAVSBDUQVIITAVFVHUJZUKFVEVGLULUMVJVLVMLVJVBDVKVCEVEVG
VDADEPZVIHTVCNAVFVHUNVTUOSUPAWAVBURPHVBDEVDUSUMUTVA $.
cthinc co wf weq elequ2 wral simprr rspcdva mofmo simprl elsetchom mpbird
syl ccat setccat isthincd eqeltrd ) ACDUAMZUEGAJKDVBLVBUBMZAVBDEVBNZHUCAV
CUDAJOZDPZKOZDPZQZQZLOZVEVGVCUFPZLRVEVGVKUGZLRZVJFOZVGPZFRZVNVJVOBOPZFRZV
QBDVGBKUHVRVPFBKFUISAVSBDUJVIITAVFVHUKZULFVEVGLUMUQVJVLVMLVJVBDVKVCEVEVGV
DADEPZVIHTVCNAVFVHUNVTUOSUPAWAVBURPHVBDEVDUSUQUTVA $.
$}

${