diff --git a/set.mm b/set.mm index 6f875e720..9cb521000 100644 --- a/set.mm +++ b/set.mm @@ -38330,6 +38330,16 @@ technically classes despite morally (and provably) being sets, like ` 1 ` ( crab cv wcel wa cab df-rab ssab2 eqsstri ) ABCDBECFAGBHCABCIABCJK $. $} + ${ + $d x A $. $d x B $. $d x ph $. + rabss3d.1 $e |- ( ( ph /\ ( x e. A /\ ps ) ) -> x e. B ) $. + $( Subclass law for restricted abstraction. (Contributed by Thierry + Arnoux, 25-Sep-2017.) $) + rabss3d $p |- ( ph -> { x e. A | ps } C_ { x e. B | ps } ) $= + ( crab nfv nfrab1 cv wcel wa simprr jca ex rabid 3imtr4g ssrd ) ACBCDGZBC + EGZACHBCDIBCEIACJZDKZBLZUAEKZBLZUASKUATKAUCUEAUCLUDBFAUBBMNOBCDPBCEPQR $. + $} + ${ $d A x $. ssrab3.1 $e |- B = { x e. A | ph } $. @@ -472279,16 +472289,6 @@ Class abstractions (a.k.a. class builders) ( csn wss wcel c0 wceq wo sssn snnzg neneqd pm2.21d sneqrg jaod imp sylan2b ) ADZBDZEACFZRGHZRSHZIZABHZRBJTUCUDTUAUDUBTUAUDTRGACKLMABCNOPQ $. - ${ - $d x A $. $d x B $. $d x ph $. - rabss3d.1 $e |- ( ( ph /\ ( x e. A /\ ps ) ) -> x e. B ) $. - $( Subclass law for restricted abstraction. (Contributed by Thierry - Arnoux, 25-Sep-2017.) $) - rabss3d $p |- ( ph -> { x e. A | ps } C_ { x e. B | ps } ) $= - ( crab nfv nfrab1 cv wcel wa simprr jca ex rabid 3imtr4g ssrd ) ACBCDGZBC - EGZACHBCDIBCEIACJZDKZBLZUAEKZBLZUASKUATKAUCUEAUCLUDBFAUBBMNOBCDPBCEPQR $. - $} - $( Intersection with an intersection. (Contributed by Thierry Arnoux, 27-Dec-2016.) $) inin $p |- ( A i^i ( A i^i B ) ) = ( A i^i B ) $= @@ -755372,6 +755372,16 @@ that every function in the sequence can have a different (partial) XKYJXLYLMXJOXGVDXJOKXGLWBVTWCWEWFWDWGWHYAXSEXREXPWIXREXPWJWKWPXMEXPWLWM XIXGBWNGZXQYRXQUHDXEDBEWOWQWRWSXGXDXEWTXAXB $. $} + + ${ + $d S a $. $d T a $. + $( There is a finite number of strictly increasing sequences over finite + alphabet. (Contributed by Ender Ting, 5-Jan-2024.) $) + upwrdfi $p |- ( S e. Fin -> { a e. UpWord S | ( # ` a ) = T } e. Fin ) $= + ( cfn wcel cv chash cfv wceq cword crab cupword wrdnfi wss upwordisword + wtru ad2antrl rabss3d mptru ssfi mpan2 syl ) ADZECFZGHBIZCAJZKZUCEZUECA + LZKZUCEZCBAMUHUJUGNZUKULPZUECUIUFUDUIEUDUFEUMUEUDAOQRSUGUJTUAUB $. + $} $} $(