From 6774571e24e23afab839cc382243f259b38d2982 Mon Sep 17 00:00:00 2001 From: mazsa Date: Sun, 12 Jan 2025 14:11:26 +0100 Subject: [PATCH] undif5 to main --- set.mm | 19 ++++++------------- 1 file changed, 6 insertions(+), 13 deletions(-) diff --git a/set.mm b/set.mm index 7ed29919c..bd3025843 100644 --- a/set.mm +++ b/set.mm @@ -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.) $) @@ -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 ) ) $= @@ -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.) $)