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undif5 to main
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mazsa committed Jan 12, 2025
1 parent 4493138 commit 6774571
Showing 1 changed file with 6 additions and 13 deletions.
19 changes: 6 additions & 13 deletions set.mm
Original file line number Diff line number Diff line change
Expand Up @@ -41684,6 +41684,11 @@ disjoint classes (see ~ disjdif ). Part of proof of Corollary 6K of
( wss cun wceq cdif ssequn1 undif2 eqeq1i bitr4i ) ABCABDZBEABAFDZBEABGLKBA
BHIJ $.

$( An equality involving class union and class difference. (Contributed by
Thierry Arnoux, 26-Jun-2024.) $)
undif5 $p |- ( ( A i^i B ) = (/) -> ( ( A u. B ) \ B ) = A ) $=
( cin c0 wceq cun cdif difun2 disjdif2 eqtrid ) ABCDEABFBGABGAABHABIJ $.

$( A subset of a difference does not intersect the subtrahend. (Contributed
by Jeff Hankins, 1-Sep-2013.) (Proof shortened by Mario Carneiro,
24-Aug-2015.) $)
Expand Down Expand Up @@ -473562,11 +473567,6 @@ Class abstractions (a.k.a. class builders)
( wceq wss wa cdif c0 eqss ssdif0 anbi12i sylbbr ) ABCABDZBADZEABFGCZBAFGCZ
EABHLNMOABIBAIJK $.

$( An equality involving class union and class difference. (Contributed by
Thierry Arnoux, 26-Jun-2024.) $)
undif5 $p |- ( ( A i^i B ) = (/) -> ( ( A u. B ) \ B ) = A ) $=
( cin c0 wceq cun cdif difun2 disjdif2 eqtrid ) ABCDEABFBGABGAABHABIJ $.

$( Two ways to express equality relative to a class ` A ` . (Contributed by
Thierry Arnoux, 23-Jun-2024.) $)
indifbi $p |- ( ( A i^i B ) = ( A i^i C ) <-> ( A \ B ) = ( A \ C ) ) $=
Expand Down Expand Up @@ -581500,17 +581500,10 @@ A collection of theorems for commuting equalities (or
suceqsneq $p |- ( A e. V -> ( suc A = suc B <-> { A } = { B } ) ) $=
( wcel csuc wceq csn suc11reg sneqbg bitr4id ) ACDAEBEFABFAGBGFABHABCIJ $.

$( An equality involving class union and class difference. (Temporary: as
soon as this Mathbox only PR is accepted, I'll open a PR to place this to
the main. PM) (Contributed by Thierry Arnoux, 26-Jun-2024.) $)
undif5TEMP $p |- ( ( A i^i B ) = (/) -> ( ( A u. B ) \ B ) = A ) $=
( cin c0 wceq cun cdif difun2 disjdif2 eqtrid ) ABCDEABFBGABGAABHABIJ $.

$( Absorption of union with a singleton by difference. (Contributed by Peter
Mazsa, 24-Jul-2024.) $)
sucdifsn2 $p |- ( ( A u. { A } ) \ { A } ) = A $=
( csn cin c0 wceq cun cdif disjcsn undif5TEMP ax-mp ) AABZCDEAKFKGAEAHAKIJ
$.
( csn cin c0 wceq cun cdif disjcsn undif5 ax-mp ) AABZCDEAKFKGAEAHAKIJ $.

$( The difference between the successor and the singleton of a class is the
class. (Contributed by Peter Mazsa, 20-Sep-2024.) $)
Expand Down

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