set-mathml.mmts

$( Metamath-MathML Presentation Typesetting for set.mm, with MathJax rendering $)

$( The idea behind Metamath "structural" typesetting is to use the formula as a
   structure rather than a list of tokens. 
   Therefore a correspondence is provided for a list of schemes, rather than 
   for the tokens. A scheme consists in a metamath formula, possibly including 
   variables (e.g. ` A ` ), and a translation text, where variables can occur
   between # signs (e.g. #A# ).

	 Unification is done top-down, and checks for the schemes in sequence.
	 It stops as soon as a matching scheme is found, therefore specific schemes
	 shall be listed first, and generic ones last.

   This is used here for presentation MathML, but the same could be used for
   any translation.

	 In this version, 
	 - by default brackets are present in class infix operations ( A F B ).
	 - they are removed in cases where they can be omitted.
   $)

$( Terminal types - when diplaying tokens or in-comment math, only try those types $)
$u wff class setvar $.

$( No brackets and extra space for top level statements $)
$s |- ( ph -> ps ) $: <mrow> <mo mathcolor=#CCC>&vdash;</mo> #ph# <mo linebreak=goodbreak lspace=1em rspace=1em href="wi.html">&rarr;</mo> #ps# </mrow> $.
$s |- ( ph <-> ps ) $: <mrow> <mo mathcolor=#CCC>&vdash;</mo> #ph# <mo linebreak=goodbreak lspace=1em rspace=1em href="df-bi.html">&harr;</mo> #ps# </mrow> $.

$( Representation for a provable statement - usually the top level statement to
   be represented. $)
$s |- ph $: <mrow><mo mathcolor=#CCC>&vdash;</mo> #ph# </mrow> $.

$( WFF variables $)
$i wff ph $: <mi mathcolor=#008> &phi; </mi> $.
$i wff ps $: <mi mathcolor=#008> &psi; </mi> $.
$i wff ch $: <mi mathcolor=#008> &chi; </mi> $.

$i wff th $: <mi mathcolor=#008> &theta; </mi> $.
$i wff ta $: <mi mathcolor=#008> &tau; </mi> $.
$i wff et $: <mi mathcolor=#008> &eta; </mi> $.
$i wff ze $: <mi mathcolor=#008> &zeta; </mi> $.
$i wff si $: <mi mathcolor=#008> &sigma; </mi> $.
$i wff rh $: <mi mathcolor=#008> &rho; </mi> $.
$i wff mu $: <mi mathcolor=#008> &mu; </mi> $.
$i wff la $: <mi mathcolor=#008> &lambda; </mi> $.
$i wff ka $: <mi mathcolor=#008> &kappa; </mi> $.


$( Set variables, first declared as class $)
$s class x $: #x# $.

$( Set variables $)
$i setvar a $: <mi mathcolor=#800>a</mi> $.
$i setvar b $: <mi mathcolor=#800>b</mi> $.
$i setvar c $: <mi mathcolor=#800>c</mi> $.
$i setvar d $: <mi mathcolor=#800>d</mi> $.
$i setvar e $: <mi mathcolor=#800>e</mi> $.
$i setvar f $: <mi mathcolor=#800>f</mi> $.
$i setvar g $: <mi mathcolor=#800>g</mi> $.
$i setvar h $: <mi mathcolor=#800>h</mi> $.
$i setvar i $: <mi mathcolor=#800>i</mi> $.
$i setvar j $: <mi mathcolor=#800>j</mi> $.
$i setvar k $: <mi mathcolor=#800>k</mi> $.
$i setvar l $: <mi mathcolor=#800>l</mi> $.
$i setvar m $: <mi mathcolor=#800>m</mi> $.
$i setvar n $: <mi mathcolor=#800>n</mi> $.
$i setvar o $: <mi mathcolor=#800>o</mi> $.
$i setvar p $: <mi mathcolor=#800>p</mi> $.
$i setvar q $: <mi mathcolor=#800>q</mi> $.
$i setvar r $: <mi mathcolor=#800>r</mi> $.
$i setvar s $: <mi mathcolor=#800>s</mi> $.
$i setvar t $: <mi mathcolor=#800>t</mi> $.
$i setvar u $: <mi mathcolor=#800>u</mi> $.
$i setvar v $: <mi mathcolor=#800>v</mi> $.
$i setvar w $: <mi mathcolor=#800>w</mi> $.
$i setvar x $: <mi mathcolor=#800>x</mi> $.
$i setvar y $: <mi mathcolor=#800>y</mi> $.
$i setvar z $: <mi mathcolor=#800>z</mi> $.

$( Class variables $)
$i class A $: <mi mathcolor=#808>A</mi> $.
$i class B $: <mi mathcolor=#808>B</mi> $.
$i class C $: <mi mathcolor=#808>C</mi> $.
$i class D $: <mi mathcolor=#808>D</mi> $.
$i class E $: <mi mathcolor=#808>E</mi> $.
$i class F $: <mi mathcolor=#808>F</mi> $.
$i class G $: <mi mathcolor=#808>G</mi> $.
$i class H $: <mi mathcolor=#808>H</mi> $.
$i class I $: <mi mathcolor=#808>I</mi> $.
$i class J $: <mi mathcolor=#808>J</mi> $.
$i class K $: <mi mathcolor=#808>K</mi> $.
$i class L $: <mi mathcolor=#808>L</mi> $.
$i class M $: <mi mathcolor=#808>M</mi> $.
$i class N $: <mi mathcolor=#808>N</mi> $.
$i class O $: <mi mathcolor=#808>O</mi> $.
$i class P $: <mi mathcolor=#808>P</mi> $.
$i class Q $: <mi mathcolor=#808>Q</mi> $.
$i class R $: <mi mathcolor=#808>R</mi> $.
$i class S $: <mi mathcolor=#808>S</mi> $.
$i class T $: <mi mathcolor=#808>T</mi> $.
$i class U $: <mi mathcolor=#808>U</mi> $.
$i class V $: <mi mathcolor=#808>V</mi> $.
$i class W $: <mi mathcolor=#808>W</mi> $.
$i class X $: <mi mathcolor=#808>X</mi> $.
$i class Y $: <mi mathcolor=#808>Y</mi> $.
$i class Z $: <mi mathcolor=#808>Z</mi> $.
$i class ./\ $: <munder accentunder><mi mathcolor=#808>&and;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .\/ $: <munder accentunder><mi mathcolor=#808>&or;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .<_ $: <munder accentunder><mi mathcolor=#808>&le;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .< $: <munder accentunder><mi mathcolor=#808>&lt;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .+ $: <munder accentunder><mi mathcolor=#808>+</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .- $: <munder accentunder><mi mathcolor=#808>-</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .X. $: <munder accentunder><mi mathcolor=#808>&times;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class ./ $: <munder accentunder><mi mathcolor=#808>&times;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .^ $: <munder accentunder><mi mathcolor=#808>&times;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .0. $: <munder accentunder><mi mathcolor=#808>0</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .1. $: <munder accentunder><mi mathcolor=#808>1</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .|| $: <munder accentunder><mi mathcolor=#808>&#8741;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .~ $: <munder accentunder><mi mathcolor=#808>&#x223C;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class ._|_ $: <munder accentunder><mi mathcolor=#808>&#8869;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .+^ $: <munder accentunder><mi mathcolor=#808>&#x2A23;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .+b $: <munder accentunder><mi mathcolor=#808>&#x271A;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .(+) $: <munder accentunder><mi mathcolor=#808>&#x2295;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .* $: <munder accentunder><mi mathcolor=#808>&lowast;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .x. $: <munder accentunder><mi mathcolor=#808>&middot;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .xb $: <munder accentunder><mi mathcolor=#808>&#x2219;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class ., $: <munder accentunder><mi mathcolor=#808>,</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .(x) $: <munder accentunder><mi mathcolor=#808>&#x2297;</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.
$i class .0b $: <munder accentunder><mi mathcolor=#808>&#x1D7CE</mi> <mo mathcolor=#808>&#x02D9;</mo></munder> $.

$( Constants $)
$s wff T. $: <mi href="df-tru.html">&#x22A4;</mi> $. $( There is actually an entity &true; $)
$s wff F. $: <mi href="df-fal.html">&#x22A5;</mi> $. $( There is actually an entity &false; $)
$s class _V $: <mi href="df-v.html" mathvariant="normal">V</mi> $.
$s class (/) $: <mi href="df-nul.html">&empty;</mi> $. $( &empty; or &#x2205; looks like a zero, &#x00D8; looks like an O, &#x2300; is actually a diameter $)
$s class Undef $: <mi href="df-undef.html">Undef</mi> $.
$s class _E $: <mi href="df-eprel.html" mathvariant="normal">E</mi> $.
$s class _I $: <mi href="df-id.html" mathvariant="normal">I</mi> $.
$s class O(1) $: <mrow href="df-o1.html"><mo>&#x1D442;</mo><mo>&ApplyFunction;</mo><mfenced><mn>1</mn></mfenced></mrow> $.
$s class <_O(1) $: <mrow href="df-lo1.html"><mo>&le;</mo><mo>&#x1D442;</mo><mo>&ApplyFunction;</mo><mfenced><mn>1</mn></mfenced></mrow> $.
$s class odZ $: <msub href="df-odz.html"><mi>od</mi><mi>&#8484;</mi></msub> $.

$( Ordinals $)
$s class 1o $: <msub href="df-1o.html"> <mn>1</mn> <mo>&#x1D45C;</mo> </msub> $.
$s class 2o $: <msub href="df-2o.html"> <mn>2</mn> <mo>&#x1D45C;</mo> </msub> $.
$s class 3o $: <msub href="df-3o.html"> <mn>3</mn> <mo>&#x1D45C;</mo> </msub> $.
$s class 4o $: <msub href="df-4o.html"> <mn>4</mn> <mo>&#x1D45C;</mo> </msub> $.

$s class On $: <mi href="df-on.html">On</mi> $.
$s class _om $: <mi href="df-om.html" mathvariant="normal">&omega;</mi> $.
$s class aleph $: <mi href="df-aleph.html">&aleph;</mi> $.
$s class CNF $: <mi href="df-cnf.html">CNF</mi> $.
$s class TC $: <mi href="df-tc.html">TC</mi> $.
$s class R1 $: <msub href="df-r1.html"><mi>R</mi><mn>1</mn></msub> $.
$s class rank $: <mi href="df-rank.html">rank</mi> $.
$s class card $: <mi href="df-card.html">card</mi> $.
$s class cf $: <mi href="df-cf.html">cf</mi> $.
$s wff CHOICE $: <mi href="df-ac.html">CHOICE</mi> $.
$s class Fin1a $: <msup href="df-fin1a.html"><mi>Fin</mi><mn>Ia</mn></msup> $.
$s class Fin2 $: <msup href="df-fin2.html"><mi>Fin</mi><mn>II</mn></msup> $.
$s class Fin3 $: <msup href="df-fin3.html"><mi>Fin</mi><mn>III</mn></msup> $.
$s class Fin4 $: <msup href="df-fin4.html"><mi>Fin</mi><mn>IV</mn></msup> $.
$s class Fin5 $: <msup href="df-fin5.html"><mi>Fin</mi><mn>V</mn></msup> $.
$s class Fin6 $: <msup href="df-fin6.html"><mi>Fin</mi><mn>VI</mn></msup> $.
$s class Fin7 $: <msup href="df-fin7.html"><mi>Fin</mi><mn>VII</mn></msup> $.
$s class GCH $: <mi href="df-gch.html">GCH</mi> $.
$s class InaccW $: <msub href="df-wina.html"><mi>Inacc</mi> <mo>&#x1D464;</mo></msub> $.
$s class Inacc $: <mi href="df-ina.html">Inacc</mi> $.
$s class WUni $: <mi href="df-wun.html">WUni</mi> $.
$s class wUniCl $: <mi href="df-wunc.html">wUniCl</mi> $.
$s class Tarski $: <mi href="df-tsk.html">Tarski</mi> $.
$s class Univ $: <mi href="df-gru.html">Univ</mi> $.
$s class tarskiMap $: <mi href="df-tskm.html">tarskiMap</mi> $.

$( Temporary constants used in the construction of ` CC ` $)
$s class N. $: <mi href="df-ni.html">&#x1d475;</mi> $.
$s class +N $: <msub href="df-pli.html"> <mo>+</mo> <mo>&#x1d475;</mo> </msub> $.
$s class .N $: <msub href="df-mi.html"> <mo>&sdot;</mo> <mo>&#x1d475;</mo> </msub> $.
$s class <N $: <msub href="df-lti.html"> <mo>&lt;</mo> <mo>&#x1d475;</mo> </msub> $.
$s class +pQ $: <msub href="df-plpq.html"> <mo>+</mo> <mi>&#x1d45d;&#x1d478;</mi> </msub> $.
$s class .pQ $: <msub href="df-mpq.html"> <mo>&sdot;</mo> <mi>&#x1d45d;&#x1d478;</mi> </msub> $.
$s class <pQ $: <msub href="df-ltpq.html"> <mo>&lt;</mo> <mi>&#x1d45d;&#x1d478;</mi> </msub> $.
$s class ~Q $: <msub href="df-enq.html"> <mo>~</mo> <mi>&#x1d478;</mi> </msub> $.
$s class Q. $: <mi href="df-nq.html">&#x1d478;</mi> </msub> $.
$s class 1Q $: <msub href="df-1nq.html"> <mn>1</mn> <mi>&#x1d478;</mi> </msub> $.
$s class /Q $: <msub href="df-erq.html"> <mo>/</mo> <mi>&#x1d478;</mi> </msub> $.
$s class +Q $: <msub href="df-plq.html"> <mo>+</mo> <mi>&#x1d478;</mi> </msub> $.
$s class .Q $: <msub href="df-mq.html"> <mo>&sdot;</mo> <mi>&#x1d478;</mi> </msub> $.
$s class *Q $: <msub href="df-rq.html"> <mo>*</mo> <mi>&#x1d478;</mi> </msub> $.
$s class <Q $: <msub href="df-ltnq.html"> <mo>&lt;</mo> <mi>&#x1d478;</mi> </msub> $.
$s class P. $: <mi href="df-np.html">&#x1d477;</mi> </msub> $.
$s class 1P $: <msub href="df-1p.html"> <mn>1</mn> <mi>&#x1d477;</mi> </msub> $.
$s class +P. $: <msub href="df-plp.html"> <mo>+</mo> <mi>&#x1d477;</mi> </msub> $.
$s class .P. $: <msub href="df-mp.html"> <mo>&sdot;</mo> <mi>&#x1d477;</mi> </msub> $.
$s class <P $: <msub href="df-ltp.html"> <mo>&lt;</mo> <mi>&#x1d477;</mi> </msub> $.
$s class ~R $: <msub href="df-enr.html"> <mo>~</mo> <mi>&#x1d479;</mi> </msub> $.
$s class R. $: <mi href="df-nr.html">&#x1d479;</mi> $.
$s class 0R $: <msub href="df-0r.html"> <mn>0</mn> <mi>&#x1d479;</mi> </msub> $.
$s class 1R $: <msub href="df-1r.html"> <mn>1</mn> <mi>&#x1d479;</mi> </msub> $.
$s class -1R $: <msub href="df-m1r.html"> <mn>-1</mn> <mi>&#x1d479;</mi> </msub> $.
$s class +R $: <msub href="df-plr.html"> <mo>+</mo> <mi>&#x1d479;</mi> </msub> $.
$s class .R $: <msub href="df-mr.html"> <mo>&sdot;</mo> <mi>&#x1d479;</mi> </msub> $.
$s class <R $: <msub href="df-ltr.html"> <mo>&lt;</mo> <mi>&#x1d479;</mi> </msub> $.

$( Strutures $)
$s class Slot A $: <mrow><mi href="df-cnfld.html">Slot</mi> #A# </mrow> $.
$s class |`s $: <msub href="df-ress.html"><mo>&uharr;</mo> <mi>&#x1D460;</mi></msub> $.
$s class +g $: <msub href="df-plusg.html"> <mo>+</mo> <mi>&#x1D454;</mi> </msub> $.
$s class +f $: <msub href="df-plusf.html"> <mo>+</mo> <mi>&#x1D453;</mi> </msub> $.
$s class 0g $: <msub href="df-0g.html"> <mn>0</mn> <mi>&#x1D454;</mi> </msub> $.
$s class -g $: <msub href="df-sbg.html"> <mo>-</mo> <mi>&#x1D454;</mi> </msub> $.
$s class .g $: <msub href="df-mulg.html"> <mn>&sdot;</mn> <mi>&#x1D454;</mi> </msub> $.
$s class .r $: <msub href="df-mulr.html"> <mo>&sdot;</mo> <mi>&#x1D45F;</mi> </msub> $.
$s class *r $: <msub href="df-starv.html"> <mo>&lowast;</mo> <mi>&#x1D45F;</mi> </msub> $.
$s class .s $: <msub href="df-vsca.html"> <mo>&sdot;</mo> <mi>&#x1D460;</mi> </msub> $.
$s class .i $: <msub href="df-ip.html"> <mo>&sdot;</mo> <mi>&#x1D456;</mi> </msub> $.
$s class |`t $: <msub href="df-rest.html"><mo>&uharr;</mo> <mi>&#x1D461;</mi></msub> $.
$s class Xt_ $: <msub href="df-pt.html"><mo>&prod;</mo> <mi>&#x1D461;</mi></msub> $.
$s class Xs_ $: <msub href="df-prds.html"><mo>&#x2a09;</mo> <mi>&#x1D460;</mi></msub> $.
$s class ^s $: <msub href="df-pws.html"><mo>&uarr;</mo> <mi>&#x1D460;</mi></msub> $.
$s class RR*s $: <msubsup href="df-xrs.html"><mo>&Ropf;</mo> <mi>&#x1D460;</mi> <mo>*</mo></msubsup> $.
$s class "s $: <msub href="df-imas.html"><mo>&ldquo;</mo> <mi>&#x1D460;</mi></msub> $.
$s class /s $: <msub href="df-divs.html"><mo>/</mo> <mi>&#x1D460;</mi></msub> $.
$s class Xs. $: <msub href="df-xps.html"><mo>&times;</mo> <mi>&#x1D460;</mi></msub> $.
$s class |`v $: <msub href="df-resv.html"><mo>&uharr;</mo> <mi>&#x1D463;</mi></msub> $.

$s class *rf $: <msub href="df-staf.html"> <mo>&lowast;</mo> <mi>&#x1D45F;&#x1D453;</mi> </msub> $.
$s class *Ring $: <mi href="df-srng.html">*-Ring</mi> $.
$s class .sf $: <msub href="df-scaf.html"> <mo>&sdot;</mo> <mi>&#x1D460;&#x1D453;</mi> </msub> $.
$s class ~=m $: <msub href="df-lmic.html"> <mo>&#x2243;</mo> <mi>&#x1D45A;</mi> </msub> $.

$s class *Met $: <mi href="df-xmet.html">&infin;Met</mi> $.
$s class *MetSp $: <mi href="df-xms.html">&infin;MetSp</mi> $.
$s class Z/nZ $: <mi href="df-zn.html">&Zopf;/n&Zopf;</mi> $.
$s class CCfld $:  <msub href="df-cnfld.html"> <mi>&Copf;</mi> <mi>fld</mi> </msub>  $.
$s class RRfld $:  <msub href="df-refld.html"> <mi>&Ropf;</mi> <mi>fld</mi> </msub>  $.
$s class ZZring $:  <msub href="df-zring.html"> <mi>&Zopf;</mi> <mi>ring</mi> </msub>  $.
$s class CHil $: <mi href="df-hl.html">&Copf;Hil</mi> $.
$s class CVec $: <mi href="df-cvs.html">&Copf;Vec</mi> $.
$s class EEhil $: <msub href="df-ehl.html"> <mi>&Eopf;</mi> <mi>hil</mi> </msub>  $.
$s class RR^ $: <mi href="df-rrx.html">&Ropf;&uarr;</mi>  $.
$s class ( RR^ ` A ) $: <msup><mi href="df-rrx.html"> #A# </msup>  $.



$s class invg $: <msub href="df-minusg.html"><mo>inv</mo> <mo>g</mo></msub> $.
$s class invr $: <msub href="df-invr.html"><mo>inv</mo> <mi>r</mi></msub> $.
$s class ~=g $: <msub href="df-gic.html"><mo>&simeq;</mo> <mo>&#x1D454;</mo></msub> $.
$s class oppG $: <msub href="df-oppg.html"><mo>opp</mo> <mo>&#x1D454;</mo></msub> $.
$s class oppR $: <msub href="df-oppr.html"><mo>opp</mo> <mi>r</mi></msub> $.
$s class proj1 $: <msub href="df-pj1.html"><mo>proj</mo> <mn>1</mn></msub> $.
$s class ~QG $: <msub href="df-eqg.html"><mo>~</mo> <mi mathvariant="italic">QG</mi></msub> $.
$s class ~FG $: <msub href="df-efg.html"><mo>~</mo> <mi mathvariant="italic">FG</mi></msub> $.
$s class varFMnd $: <msub href="df-vrmd.html"><mo>var</mo> <mi mathvariant="italic">FMnd</mi></msub> $.
$s class varFGrp $: <msub href="df-vrgp.html"><mo>var</mo> <mi mathvariant="italic">FGrp</mi></msub> $.
$s class 1r $: <msub href="df-ur.html"><mn>1</mn> <mi>r</mi></msub> $.
$s class ||r $: <msub href="df-dvdsr.html"><mo>&par;</mo> <mi>r</mi></msub> $.
$s class /r $: <msub href="df-dvr.html"><mo>/</mo> <mi>r</mi></msub> $.

$( Category Theory $)
$s class Homf $: <msub href="df-homf.html"><mi>Hom</mi> <mi>&#x1D453;</mi></msub> $.
$s class comf $: <msub href="df-comf.html"><mi>comp</mi> <mi>&#x1D453;</mi></msub> $.
$s class C_cat $: <msub href="df-ssc.html"><mo>&sube;</mo> <mi>cat</mi></msub> $.
$s class |`cat $: <msub href="df-resc.html"><mo>&uharr;</mo> <mi>cat</mi></msub> $.
$s class idFunc $: <msub href="df-idfu.html"><mo>id</mo> <mi>func</mi></msub> $.
$s class o.func $: <msub href="df-cofu.html"><mo>&compfn;</mo> <mi>func</mi></msub> $.
$s class |`f $: <msub href="df-resf.html"><mo>&uharr;</mo> <mi>f</mi></msub> $.
$s class domA $: <msub href="df-doma.html"><mo>dom</mo> <mi>a</mi></msub> $.
$s class codA $: <msub href="df-coda.html"><mo>cod</mo> <mi>a</mi></msub> $.
$s class HomA $: <msub href="df-homa.html"><mo>Hom</mo> <mi>a</mi></msub> $.
$s class IdA $: <msub href="df-ida.html"><mo>Id</mo> <mi>a</mi></msub> $.
$s class compA $: <msub href="df-coa.html"><mo>comp</mo> <mi>a</mi></msub> $.
$s class Xc. $: <msub href="df-xpc.html"><mo>&times;</mo> <mi>c</mi></msub> $.
$s class 1stF $: <msub href="df-1stf.html"><msup><mo>1</mo> <mo>st</mo></msup> <mi>F</mi></msub> $.
$s class 2ndF $: <msub href="df-2ndf.html"><msup><mo>2</mo> <mo>nd</mo></msup> <mi>F</mi></msub> $.
$s class pairF $: <msub href="df-prf.html"><mo>&lang;,&rang;</mo> <mi>F</mi></msub> $.
$s class evalF $: <msub href="df-evlf.html"><mo>eval</mo> <mi>F</mi></msub> $.
$s class curryF $: <msub href="df-curf.html"><mo>curry</mo> <mi>F</mi></msub> $.
$s class uncurryF $: <msub href="df-uncf.html"><mo>uncurry</mo> <mi>F</mi></msub> $.
$s class DiagFunc $: <msub href="df-diag.html"><mo>&Delta;</mo> <mi>func</mi></msub> $.
$s class HomF $: <msub href="df-hof.html"><mo>Hom</mo> <mi>F</mi></msub> $.
$s class Yon $: <mi href="df-yon.html">Yon</mi> $.

$s class RngCat $: <mi href="df-rngc.html">RngCat</mi> $.
$s class RingCat $: <mi href="df-ringc.html">RingCat</mi> $.
$s class ExtStrCat $: <mi href="df-estrc.html">ExtStrCat</mi> $.

$s class RngCatALTV $: <mi href="df-rngcALTV.html">RngCatALTV</mi> $.
$s class RingCatALTV $: <mi href="df-ringcALTV.html">RingCatALTV</mi> $.

$s class InitO $: <mi href="df-inito.html">InitO</mi> $.
$s class TermO $: <mi href="df-termo.html">TermO</mi> $.
$s class ZeroO $: <mi href="df-zeroo.html">ZeroO</mi> $.


$s class 0. $: <mi href="df-p0.html">0.</mi> $.
$s class 1. $: <mi href="df-p1.html">1.</mi> $.
$s class lastS $: <mi href="df-lswrd.html">lastS</mi> $.
$s class repeatS $: <mi href="df-reps.html">repeatS</mi> $.
$s class cyclShift $: <mi href="df-csh.html">cyclShift</mi> $.
$s class <bag $: <msub href="df-ltbag.html"><mo>&lt;</mo> <mo>bag</mo></msub> $.

$( Analysis $)
$s class NN $: <mi href="df-nn.html"> &Nopf; </mi> $.
$s class ZZ $: <mi href="df-z.html"> &Zopf; </mi> $.
$s class NN0 $: <msub href="df-n0.html"> <mi> &Nopf; </mi><mn> 0 </mn></msub> $.
$s class NN0* $: <msubsup href="df-n0.html"> <mi> &Nopf; </mi><mn> 0 </mn><mo> * </mo></msubsup> $.
$s class QQ $: <mi href="df-q.html"> &Qopf; </mi> $.
$s class RR $: <mi href="df-r.html"> &Ropf; </mi> $.
$s class RR* $: <msup href="df-xr.html"> <mi> &Ropf; </mi><mo> * </mo></msup> $.
$s class RR+ $: <msup href="df-rp.html"> <mi> &Ropf; </mi><mo> + </mo></msup> $.
$s class CC $: <mi href="df-c.html"> &Copf; </mi> $.
$s class Z[i] $: <mrow href="df-gz.html"> <mi>&Zopf;</mi> <mfenced open="[" close="]"><mi>i</mi></mfenced> </mrow> $.
$s class L^1 $: <msup href="df-ibl.html"> <mi>&#x1D43F;</mi> <mn>1</mn> </msup> $.
$s class Fin $: <mi href="df-fin.html">Fin</mi> $.
$s class +oo $: <mi href="df-pnf.html">+&infin;</mi> $.
$s class -oo $: <mi href="df-mnf.html">&minus;&infin;</mi> $.
$s class 0p $: <msub href="df-0p.html"> <mn>0</mn> <mo>&#x1d45d;</mo> </msub> $.
$s class 1/_G $: <mfrac href="df-igam.html"><mn>1</mn> <mi mathvariant="normal">&Gamma;</mi></mfrac> $.

$( Number-theoretical functions $)
$s class ppi $: <munder href="df-ppi.html"><mo>&pi;</mo> <mo>&#x5F;</mo></munder> $. 
$s class theta $: <mi href="df-cht.html">&theta;</mi> $.
$s class Lam $: <mi href="df-vma.html">&Lambda;</mi> $.
$s class psi $: <mi href="df-chp.html">&psi;</mi> $.
$s class mmu $: <mi href="df-mu.html">&mu;</mi> $.
$s class sigma $: <mi href="df-sgm.html"> &sigma; </mi> $.
$s class #p $: <msub href="df-prmo.html"><mi> # </mi> <mi> p </mi></msub> $.


$s class 1stc $: <mrow href="df-1stc.html"> <msup><mo>1</mo> <mo>st</mo></msup> <mi>&#x1D714;</mi> </mrow> $. $( math italic omega $)
$s class 2ndc $: <mrow href="df-2ndc.html"> <msup><mo>2</mo> <mo>nd</mo></msup> <mi>&#x1D714;</mi> </mrow> $. $( math italic omega $)

$( Geometry $)
$s class TarskiG $: <msub href="df-trkg.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi></msub> $.
$s class TarskiGC $: <msubsup href="df-trkgc.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi> <mi>C</mi></msubsup> $.
$s class TarskiGB $: <msubsup href="df-trkgb.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi> <mi>B</mi></msubsup> $.
$s class TarskiGCB $: <msubsup href="df-trkgcb.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi> <mi>CB</mi></msubsup> $.
$s class TarskiGDim>= $: <mrow href="df-trkgld.html"><msub><mi>Dim</mi> <mi>&#x1d4a2;</mi></msub> <mo>&ge;</mo></mrow> $.
$s class TarskiG2D $: <msubsup href="df-trkg2d.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi> <mi>2D</mi></msubsup> $.
$s class TarskiGE $: <msubsup href="df-trkge.html"><mo>&#x1d4a2;</mo> <mi>Tarski</mi> <mi>E</mi></msubsup> $.
$s class Itv $: <mi href="df-itv.html"> Itv </mi> $.
$s class LineG $: <msub href="df-lineg.html"><mo>Line</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class cgrG $: <msub href="df-cgrg.html"><mo>&#x223C;</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class leG $: <msub href="df-leg.html"><mo>&le;</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class hlG $: <msub href="df-hlg.html"><mo>hl</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class midG $: <msub href="df-mid.html"><mo>mid</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class pInvG $: <msub href="df-mir.html"><mo>pInv</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class lInvG $: <msub href="df-lmi.html"><mo>lInv</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class raG $: <msub href="df-rag.html"><mo>&angrt;</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class perpG $: <msub href="df-perp.html"><mo>&#x27C2;</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class cgrA $: <msubsup href="df-cgra.html"><mo>&#x223C;</mo> <mo>&#x1d4a2;</mo> <mo>&ang;</mo></msubsup> $.
$s class inA $: <msubsup href="df-inag.html"><mo>&isin;</mo> <mo>&#x1d4a2;</mo> <mo>&ang;</mo></msubsup> $.
$s class leA $: <msubsup href="df-leag.html"><mo>&le;</mo> <mo>&#x1d4a2;</mo> <mo>&ang;</mo></msubsup> $.
$s class eqltrG $: <msub href="df-eqlg.html"><mo>Equilaterals</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class toTG $: <msub href="df-ttg.html"><mo>to&#x1d4a2;</mo> <mi>Tarski</mi></msub> $.
$s class EEG $: <msub href="df-eeg.html"><mo>&Eopf;</mo> <mo>&#x1d4a2;</mo></msub> $.
$s class AFS $: <mo href="df-afs.html">AFS</mo> $.
$s class Ismt $: <mo href="df-ismt.html">Ismt</mo> $.
$s class hpG $: <msub href="df-hpg.html"><mo>hp</mo> <mo>&#x1d4a2;</mo></msub> $.


$( Commented out in set.mm

$s class supw $: <msub href="df-spw.html"><mo>sup</mo> <mo>w</mo></msub> $.
$s class infw $: <msub href="df-nfw.html"><mo>inf</mo> <mo>w</mo></msub> $.
$s class ceiling $: <mi href="df-ceiling.html">&#8968;</mi> $.
$s class LatRel $: <mi href="df-lar.html">LatRel</mi> $.
$)


$( Constant classes with simple "mi" rules 
   (this part has been generated from the althtmldef rules of set.mm) $)
$s class On $: <mi href="df-on.html">On</mi> $.
$s class Undef $: <mi href="df-undef.html">Undef</mi> $.
$s class Fin $: <mi href="df-fin.html">Fin</mi> $.
$s class fi $: <mi href="df-fi.html">fi</mi> $.
$s class har $: <mi href="df-har.html">har</mi> $.
$s class CNF $: <mi href="df-cnf.html"> CNF </mi> $.
$s class TC $: <mi href="df-tc.html">TC</mi> $.
$s class rank $: <mi href="df-rank.html">rank</mi> $.
$s class card $: <mi href="df-card.html">card</mi> $.
$s class aleph $: <mi href="df-aleph.html">&#8501;</mi> $.
$s class cf $: <mi href="df-cf.html">cf</mi> $.
$s class Inacc $: <mi href="df-ina.html">Inacc</mi> $.
$s class WUni $: <mi href="df-wun.html">WUni</mi> $.
$s class wUniCl $: <mi href="df-wunc.html">wUniCl</mi> $.
$s class Tarski $: <mi href="df-tsk.html">Tarski</mi> $.
$s class Univ $: <mi href="df-gru.html">Univ</mi> $.
$s class tarskiMap $: <mi href="df-tskm.html">tarskiMap</mi> $.
$s class supp $: <mi href="df-supp.html">supp</mi> $.
$s class finSupp $: <mi href="df-supp.html">finSupp</mi> $.
$s class CC $: <mi href="df-c.html">&#8450;</mi> $.
$s class RR $: <mi href="df-r.html">&#8477;</mi> $.
$s class _i $: <mi href="df-i.html" mathvariant="normal">i</mi> $. $( There is actually an entity &ImaginaryI; $)
$s class NN $: <mi href="df-nn.html">&#8469;</mi> $.
$s class ZZ $: <mi href="df-z.html">&#8484;</mi> $.
$s class QQ $: <mi href="df-q.html">&#8474;</mi> $.
$s class mod $: <mi href="df-mod.html"> mod </mi> $.
$s class ++ $: <mi href="df-concat.html"> ++ </mi> $.
$s class substr $: <mi href="df-substr.html"> substr </mi> $.
$s class splice $: <mi href="df-splice.html"> splice </mi> $.
$s class reverse $: <mi href="df-reverse.html">reverse</mi> $.
$s class shift $: <mi href="df-shft.html">shift</mi> $.
$s class Re $: <mi href="df-re.html">&real;</mi> $.
$s class Im $: <mi href="df-im.html">&image;</mi> $.
$s class sqrt $: <mi href="df-sqrt.html">&radic;</mi> $.
$s class abs $: <mi href="df-abs.html">abs</mi> $.
$s class limsup $: <mi href="df-limsup.html">lim sup</mi> $.
$s class exp $: <mi href="df-ef.html">exp</mi> $.
$s class _e $: <mi href="df-e.html" mathvariant="normal">e</mi> $.
$s class sin $: <mi href="df-sin.html">sin</mi> $.
$s class cos $: <mi href="df-cos.html">cos</mi> $.
$s class tan $: <mi href="df-tan.html">tan</mi> $.
$s class _pi $: <mi href="df-pi.html" mathvariant="normal">&pi;</mi> $.
$s class bits $: <mi href="df-bits.html">bits</mi> $.
$s class sadd $: <mi href="df-sad.html">sadd</mi> $.
$s class smul $: <mi href="df-smu.html">smul</mi> $.
$s class gcd $: <mi href="df-gcd.html">gcd</mi> $.
$s class Prime $: <mi href="df-prm.html">&#8473;</mi> $.
$s class numer $: <mi href="df-numer.html">numer</mi> $.
$s class denom $: <mi href="df-denom.html">denom</mi> $.
$s class phi $: <mi href="df-phi.html" mathvariant="normal">&#981;</mi> $.
$s class pCnt $: <mi href="df-pc.html">pCnt</mi> $.
$s class AP $: <mi href="df-vdwap.html">AP</mi> $.
$s class MonoAP $: <mi href="df-vdwmc.html">MonoAP</mi> $.
$s class PolyAP $: <mi href="df-vdwpc.html">PolyAP</mi> $.
$s class Ramsey $: <mi href="df-ram.html">Ramsey</mi> $.
$s class Struct $: <mi href="df-struct.html">Struct</mi> $.
$s class ndx $: <mi href="df-ndx.html">ndx</mi> $.
$s class sSet $: <mi href="df-sets.html">sSet</mi> $.
$s class Base $: <mi href="df-base.html">Base</mi> $.
$s class Scalar $: <mi href="df-sca.html">Scalar</mi> $.
$s class TopSet $: <mi href="df-tset.html">TopSet</mi> $.
$s class le $: <mi href="df-ple.html">le</mi> $.
$s class oc $: <mi href="df-ocomp.html">oc</mi> $.
$s class dist $: <mi href="df-ds.html">dist</mi> $.
$s class Hom $: <mi href="df-linm.html">Hom</mi> $.
$s class comp $: <mi href="df-cco.html">comp</mi> $.
$s class TopOpen $: <mi href="df-topn.html">TopOpen</mi> $.
$s class topGen $: <mi href="df-topgen.html">topGen</mi> $.
$s class ordTop $: <mi href="df-ordt.html">ordTop</mi> $.
$s class qTop $: <mi href="df-qtop.html"> qTop </mi> $.
$s class Moore $: <mi href="df-mre.html">Moore</mi> $.
$s class mrCls $: <mi href="df-mrc.html">mrCls</mi> $.
$s class mrInd $: <mi href="df-mri.html">mrInd</mi> $.
$s class ACS $: <mi href="df-acs.html">ACS</mi> $.
$s class Cat $: <mi href="df-cat.html">Cat</mi> $.
$s class Id $: <mi href="df-cid.html">Id</mi> $.
$s class oppCat $: <mi href="df-oppc.html">oppCat</mi> $.
$s class Mono $: <mi href="df-mon.html">Mono</mi> $.
$s class Epi $: <mi href="df-epi.html">Epi</mi> $.
$s class Sect $: <mi href="df-sect.html">Sect</mi> $.
$s class Inv $: <mi href="df-inv.html">Inv</mi> $.
$s class Iso $: <mi href="df-iso.html">Iso</mi> $.
$s class Subcat $: <mi href="df-subc.html">Subcat</mi> $.
$s class Func $: <mi href="df-func.html">Func</mi> $.
$s class Full $: <mi href="df-full.html">Full</mi> $.
$s class Faith $: <mi href="df-fth.html">Faith</mi> $.
$s class Nat $: <mi href="df-nat.html">Nat</mi> $.
$s class FuncCat $: <mi href="df-fuc.html">FuncCat</mi> $.
$s class Arrow $: <mi href="df-arw.html">Arrow</mi> $.
$s class SetCat $: <mi href="df-setc.html">SetCat</mi> $.
$s class CatCat $: <mi href="df-catc.html">CatCat</mi> $.
$s class Preset $: <mi href="df-preset.html"> Preset </mi> $.
$s class Dirset $: <mi href="df-drs.html">Dirset</mi> $.
$s class Poset $: <mi href="df-poset.html">Poset</mi> $.
$s class lt $: <mi href="df-plt.html">lt</mi> $.
$s class lub $: <mi href="df-lubOLD.html">lub</mi> $.
$s class glb $: <mi href="df-glb.html">glb</mi> $.
$s class join $: <mi href="df-join.html">join</mi> $.
$s class meet $: <mi href="df-meet.html">meet</mi> $.
$s class Toset $: <mi href="df-toset.html">Toset</mi> $.
$s class Lat $: <mi href="df-lat.html">Lat</mi> $.
$s class CLat $: <mi href="df-clat.html">CLat</mi> $.
$s class ODual $: <mi href="df-odu.html">ODual</mi> $.
$s class toInc $: <mi href="df-ipo.html">toInc</mi> $.
$s class DLat $: <mi href="df-dlat.html">DLat</mi> $.
$s class PosetRel $: <mi href="df-ps.html">PosetRel</mi> $.
$s class TosetRel $: <mi href="df-tsr.html">TosetRel</mi> $.
$s class DirRel $: <mi href="df-dir.html">DirRel</mi> $.
$s class tail $: <mi href="df-tail.html">tail</mi> $.
$s class Mgm $: <mi href="df-mgm.html">Mgm</mi> $.
$s class Mnd $: <mi href="df-mnd.html">Mnd</mi> $.
$s class SGrp $: <mi href="df-sgrp.html">SGrp</mi> $.
$s class Grp $: <mi href="df-grp.html">Grp</mi> $.
$s class MgmHom $: <mi href="df-mgmhm.html"> MgmHom </mi> $.
$s class MndHom $: <mi href="df-mhm.html"> MndHom </mi> $.
$s class SubMgm $: <mi href="df-submgm.html">SubMgm</mi> $.
$s class SubMnd $: <mi href="df-submnd.html">SubMnd</mi> $.
$s class freeMnd $: <mi href="df-frmd.html">freeMnd</mi> $.
$s class SubGrp $: <mi href="df-subg.html">SubGrp</mi> $.
$s class NrmSGrp $: <mi href="df-nsg.html">NrmSGrp</mi> $.
$s class GrpHom $: <mi href="df-ghm.html"> GrpHom </mi> $.
$s class GrpIso $: <mi href="df-gim.html"> GrpIso </mi> $.
$s class GrpAct $: <mi href="df-ga.html"> GrpAct </mi> $.
$s class SymGrp $: <mi href="df-symg.html">SymGrp</mi> $.
$s class Cntz $: <mi href="df-cntz.html">Cntz</mi> $.
$s class Cntr $: <mi href="df-cntr.html">Cntr</mi> $.
$s class od $: <mi href="df-od.html">od</mi> $.
$s class gEx $: <mi href="df-gex.html">gEx</mi> $.
$s class pGrp $: <mi href="df-pgp.html"> pGrp </mi> $.
$s class pSyl $: <mi href="df-slw.html"> pSyl </mi> $.
$s class LSSum $: <mi href="df-lsm.html">LSSum</mi> $.
$s class freeGrp $: <mi href="df-frgp.html">freeGrp</mi> $.
$s class CMnd $: <mi href="df-cmn.html">CMnd</mi> $.
$s class Abel $: <mi href="df-abl.html">Abel</mi> $.
$s class CycGrp $: <mi href="df-cyg.html">CycGrp</mi> $.
$s class DProd $: <mi href="df-dprd.html"> DProd </mi> $.
$s class dProj $: <mi href="df-dpj.html">dProj</mi> $.
$s class mulGrp $: <mi href="df-mgp.html">mulGrp</mi> $.
$s class Rng $: <mi href="df-rng.html">Rng</mi> $.
$s class Ring $: <mi href="df-ring.html">Ring</mi> $.
$s class CRing $: <mi href="df-cring.html">CRing</mi> $.
$s class Unit $: <mi href="df-unit.html">Unit</mi> $.
$s class Irred $: <mi href="df-irred.html">Irred</mi> $.
$s class RngHomo $: <mi href="df-rnghomo.html"> RngHomo </mi> $.
$s class RngIsom $: <mi href="df-rngisom.html"> RngIsom </mi> $.
$s class RingHom $: <mi href="df-rnghom.html"> RingHom </mi> $.
$s class RingIso $: <mi href="df-rngiso.html"> RingIso </mi> $.
$s class ~=r $: <msub href="df-ric.html"> <mo>&#x2243;</mo> <mi>&#x1D45F;</mi> </msub> $.
$s class DivRing $: <mi href="df-drng.html">DivRing</mi> $.
$s class Field $: <mi href="df-field.html">Field</mi> $.
$s class SubRing $: <mi href="df-subrg.html">SubRing</mi> $.
$s class RingSpan $: <mi href="df-rgspn.html">RingSpan</mi> $.
$s class AbsVal $: <mi href="df-abv.html">AbsVal</mi> $.
$s class LMod $: <mi href="df-lmod.html">LMod</mi> $.
$s class LSubSp $: <mi href="df-lss.html">LSubSp</mi> $.
$s class LSpan $: <mi href="df-lsp.html">LSpan</mi> $.
$s class LMHom $: <mi href="df-lmhm.html"> LMHom </mi> $.
$s class LMIso $: <mi href="df-lmim.html"> LMIso </mi> $.
$s class LBasis $: <mi href="df-lbs.html">LBasis</mi> $.
$s class LVec $: <mi href="df-lvec.html">LVec</mi> $.
$s class subringAlg $: <mi href="df-sra.html"> subringAlg </mi> $.
$s class ringLMod $: <mi href="df-rgmod.html">ringLMod</mi> $.
$s class LIdeal $: <mi href="df-lidl.html">LIdeal</mi> $.
$s class RSpan $: <mi href="df-rsp.html">RSpan</mi> $.
$s class 2Ideal $: <mi href="df-2idl.html">2Ideal</mi> $.
$s class LPIdeal $: <mi href="df-lpidl.html">LPIdeal</mi> $.
$s class LPIR $: <mi href="df-lpir.html">LPIR</mi> $.
$s class NzRing $: <mi href="df-nzr.html">NzRing</mi> $.
$s class RLReg $: <mi href="df-rlreg.html">RLReg</mi> $.
$s class Domn $: <mi href="df-domn.html">Domn</mi> $.
$s class IDomn $: <mi href="df-idom.html">IDomn</mi> $.
$s class PID $: <mi href="df-pid.html">PID</mi> $.
$s class AssAlg $: <mi href="df-assa.html">AssAlg</mi> $.
$s class AlgSpan $: <mi href="df-asp.html">AlgSpan</mi> $.
$s class algSc $: <mi href="df-ascl.html">algSc</mi> $.
$s class mPwSer $: <mi href="df-psr.html"> mPwSer </mi> $.
$s class mVar $: <mi href="df-mvr.html"> mVar </mi> $.
$s class mPoly $: <mi href="df-mpl.html"> mPoly </mi> $.
$s class evalSub $: <mi href="df-evls.html"> evalSub </mi> $.
$s class eval $: <mi href="df-evl.html"> eval </mi> $.
$s class mHomP $: <mi href="df-mhp.html"> mHomP </mi> $.
$s class mPSDer $: <mi href="df-psd.html"> mPSDer </mi> $.
$s class ordPwSer $: <mi href="df-opsr.html"> ordPwSer </mi> $.
$s class selectVars $: <mi href="df-selv.html"> selectVars </mi> $.
$s class AlgInd $: <mi href="df-algind.html"> AlgInd </mi> $.
$s class Met $: <mi href="df-met.html">Met</mi> $.
$s class ball $: <mi href="df-bl.html">ball</mi> $.
$s class MetOpen $: <mi href="df-mopn.html">MetOpen</mi> $.
$s class chr $: <mi href="df-chr.html">chr</mi> $.
$s class PreHil $: <mi href="df-phl.html">PreHil</mi> $.
$s class ocv $: <mi href="df-ocv.html">ocv</mi> $.
$s class CSubSp $: <mi href="df-cs.html">CSubSp</mi> $.
$s class toHL $: <mi href="df-thl.html">toHL</mi> $.
$s class proj $: <mi href="df-pj.html">proj</mi> $.
$s class Hil $: <mi href="df-hil.html">Hil</mi> $.
$s class OBasis $: <mi href="df-obs.html">OBasis</mi> $.
$s class Top $: <mi href="df-top.html">Top</mi> $.
$s class TopOn $: <mi href="df-topon.html">TopOn</mi> $.
$s class TopSp $: <mi href="df-topsp.html">TopSp</mi> $.
$s class TopBases $: <mi href="df-bases.html">TopBases</mi> $.
$s class Clsd $: <mi href="df-cld.html">Clsd</mi> $.
$s class int $: <mi href="df-ntr.html">int</mi> $.
$s class cls $: <mi href="df-clsOLD.html">cls</mi> $.
$s class nei $: <mi href="df-nei.html">nei</mi> $.
$s class limPt $: <mi href="df-lp.html">limPt</mi> $.
$s class Perf $: <mi href="df-perf.html">Perf</mi> $.
$s class Cn $: <mi href="df-cn.html">Cn</mi> $.
$s class CnP $: <mi href="df-cnp.html">CnP</mi> $.
$s class Kol2 $: <mi href="df-t0.html">Kol2</mi> $.
$s class Fre $: <mi href="df-t1.html">Fre</mi> $.
$s class Haus $: <mi href="df-haus.html">Haus</mi> $.
$s class Reg $: <mi href="df-reg.html">Reg</mi> $.
$s class Nrm $: <mi href="df-nrm.html">Nrm</mi> $.
$s class CNrm $: <mi href="df-cnrm.html">CNrm</mi> $.
$s class PNrm $: <mi href="df-pnrm.html">PNrm</mi> $.
$s class Comp $: <mi href="df-cmp.html">Comp</mi> $.
$s class Conn $: <mi href="df-conn.html">Conn</mi> $.
$s class kGen $: <mi href="df-kgen.html">&#x1D458;Gen</mi> $.
$s class KQ $: <mi href="df-kq.html">KQ</mi> $.
$s class Homeo $: <mi href="df-hmeo.html">Homeo</mi> $.
$s class fBas $: <mi href="df-fbas.html">fBas</mi> $.
$s class filGen $: <mi href="df-fg.html">filGen</mi> $.
$s class Fil $: <mi href="df-fil.html">Fil</mi> $.
$s class UFil $: <mi href="df-ufil.html">UFil</mi> $.
$s class UFL $: <mi href="df-ufl.html">UFL</mi> $.
$s class FilMap $: <mi href="df-fm.html"> FilMap </mi> $.
$s class fLim $: <mi href="df-flim.html"> fLim </mi> $.
$s class fLimf $: <mi href="df-flf.html"> fLimf </mi> $.
$s class fClus $: <mi href="df-fcls.html"> fClus </mi> $.
$s class fClusf $: <mi href="df-fcf.html"> fClusf </mi> $.
$s class TopMnd $: <mi href="df-tmd.html">TopMnd</mi> $.
$s class TopGrp $: <mi href="df-tgp.html">TopGrp</mi> $.
$s class tsums $: <mi href="df-tsms.html">tsums</mi> $.
$s class TopRing $: <mi href="df-trg.html">TopRing</mi> $.
$s class TopDRing $: <mi href="df-tdrg.html">TopDRing</mi> $.
$s class TopMod $: <mi href="df-tlm.html">TopMod</mi> $.
$s class TopVec $: <mi href="df-tvc.html">TopVec</mi> $.
$s class MetSp $: <mi href="df-ms.html">MetSp</mi> $.
$s class toMetSp $: <mi href="df-tms.html">toMetSp</mi> $.
$s class norm $: <mi href="df-norm.html">norm</mi> $.
$s class NrmGrp $: <mi href="df-ngp.html">NrmGrp</mi> $.
$s class toNrmGrp $: <mi href="df-tng.html"> toNrmGrp </mi> $.
$s class NrmRing $: <mi href="df-nrg.html">NrmRing</mi> $.
$s class NrmMod $: <mi href="df-nlm.html">NrmMod</mi> $.
$s class NrmVec $: <mi href="df-nvc.html">NrmVec</mi> $.
$s class normOp $: <mi href="df-nmo.html"> normOp </mi> $.
$s class NGHom $: <mi href="df-nghm.html"> NGHom </mi> $.
$s class NMHom $: <mi href="df-nmhm.html"> NMHom </mi> $.
$s class II $: <mi href="df-ii.html">II</mi> $.
$s class Htpy $: <mi href="df-htpy.html"> Htpy </mi> $.
$s class PHtpy $: <mi href="df-phtpy.html">PHtpy</mi> $.
$s class CMod $: <mi href="df-clm.html">CMod</mi> $.
$s class CPreHil $: <mi href="df-cph.html">CPreHil</mi> $.
$s class toCHil $: <mi href="df-tch.html">toCHil</mi> $.
$s class CauFil $: <mi href="df-cfil.html">CauFil</mi> $.
$s class CauFilU $: <mi href="df-cfilu.html">CauFilU</mi> $.
$s class Cau $: <mi href="df-cau.html">Cau</mi> $.
$s class CMet $: <mi href="df-cmet.html">CMet</mi> $.
$s class CMetSp $: <mi href="df-cms.html">CMetSp</mi> $.
$s class Ban $: <mi href="df-bn.html">Ban</mi> $.
$s class mDeg $: <mi href="df-mdeg.html"> mDeg </mi> $.
$s class Poly $: <mi href="df-ply.html">Poly</mi> $.
$s class coeff $: <mi href="df-coe.html">coeff</mi> $.
$s class deg $: <mi href="df-dgr.html">deg</mi> $.
$s class quot $: <mi href="df-quot.html"> quot </mi> $.
$s class AA $: <mi href="df-aa.html">&#120120;</mi> $.
$s class Tayl $: <mi href="df-tayl.html"> Tayl </mi> $.
$s class Ana $: <mi href="df-ana.html">Ana</mi> $.
$s class DChr $: <mi href="df-dchr.html">DChr</mi> $.
$s class Plig $: <mi href="df-plig.html">Plig</mi> $.
$s class RPrime $: <mi href="df-rprm.html">RPrime</mi> $.
$s class t+ $: <mi href="df-trcl.html">t+</mi> $.
$s class t* $: <mi href="df-rtrcl.html">t*</mi> $.
$s class GrpOp $: <mi href="df-grpo.html">GrpOp</mi> $.
$s class GId $: <mi href="df-gid.html">GId</mi> $.
$s class inv $: <mi href="df-ginv.html">inv</mi> $.
$s class AbelOp $: <mi href="df-ablo.html">AbelOp</mi> $.
$s class Ass $: <mi href="df-ass.html">Ass</mi> $.
$s class ExId $: <mi href="df-exid.html"> ExId </mi> $.
$s class Magma $: <mi href="df-mgm.html">Magma</mi> $.
$s class SemiGrp $: <mi href="df-sgr.html">SemiGrp</mi> $.
$s class MndOp $: <mi href="df-mndo.html">MndOp</mi> $.
$s class GrpOpHom $: <mi href="df-ghom.html"> GrpOpHom </mi> $.
$s class RingOps $: <mi href="df-rngo.html">RingOps</mi> $.
$s class DivRingOps $: <mi href="df-drngo.html">DivRingOps</mi> $.
$s class Com2 $: <mi href="df-com2.html">Com2</mi> $.
$s class Fld $: <mi href="df-fld.html">Fld</mi> $.
$s class NrmCVec $: <mi href="df-nv.html">NrmCVec</mi> $.
$s class BaseSet $: <mi href="df-ba.html">BaseSet</mi> $.
$s class IndMet $: <mi href="df-ims.html">IndMet</mi> $.
$s class SubSp $: <mi href="df-ssp.html">SubSp</mi> $.
$s class LnOp $: <mi href="df-lno.html"> LnOp </mi> $.
$s class BLnOp $: <mi href="df-blo.html"> BLnOp </mi> $.
$s class adj $: <mi href="df-aj.html">adj</mi> $.
$s class HmOp $: <mi href="df-hmo.html">HmOp</mi> $.
$s class CBan $: <mi href="df-cbn.html">CBan</mi> $.
$s class Cauchy $: <mi href="df-hcau.html">Cauchy</mi> $.
$s class _|_ $: <mi href="df-oc.html">&#8869;</mi> $.
$s class span $: <mi href="df-span.html">span</mi> $.
$s class ContOp $: <mi href="df-cnop.html">ContOp</mi> $.
$s class LinOp $: <mi href="df-lnop.html">LinOp</mi> $.
$s class BndLinOp $: <mi href="df-bdop.html">BndLinOp</mi> $.
$s class UniOp $: <mi href="df-unop.html">UniOp</mi> $.
$s class HrmOp $: <mi href="df-hmop.html">HrmOp</mi> $.
$s class null $: <mi href="df-nlfn.html">null</mi> $.
$s class ContFn $: <mi href="df-cnfn.html">ContFn</mi> $.
$s class LinFn $: <mi href="df-lnfn.html">LinFn</mi> $.
$s class bra $: <mi href="df-bra.html">bra</mi> $.
$s class ketbra $: <mi href="df-kb.html"> ketbra </mi> $.
$s class eigvec $: <mi href="df-eigvec.html">eigvec</mi> $.
$s class eigval $: <mi href="df-eigval.html">eigval</mi> $.
$s class Lambda $: <mi href="df-spec.html">Lambda</mi> $.
$s class States $: <mi href="df-st.html">States</mi> $.
$s class CHStates $: <mi href="df-hst.html">CHStates</mi> $.
$s class HAtoms $: <mi href="df-at.html">HAtoms</mi> $.

$( Mario Carneiro's Mathbox $)

$s class gamma $: <mi href="df-em.html">&gamma;</mi> $.
$s class zeta $: <mi href="df-zeta.html" mathvariant="normal">&zeta;</mi> $.
$s class _G $: <mi href="df-gam.html" mathvariant="normal">&Gamma;</mi> $.
$s class log_G $: <mrow><mi href="df-lgam.html">log</mi> <mi href="df-gam.html" mathvariant="normal">&Gamma;</mi></mrow> $.
$s class Retr $: <mi href="df-retr.html"> Retr </mi> $.
$s class PConn $: <mi href="df-pconn.html">PConn</mi> $.
$s class SConn $: <mi href="df-sconn.html">SConn</mi> $.
$s class CovMap $: <mi href="df-cvm.html"> CovMap </mi> $.
$s class AxExt $: <mi href="df-gzext.html">AxExt</mi> $.
$s class AxRep $: <mi href="df-gzrep.html">AxRep</mi> $.
$s class AxPow $: <mi href="df-gzpow.html">AxPow</mi> $.
$s class AxUn $: <mi href="df-gzun.html">AxUn</mi> $.
$s class AxReg $: <mi href="df-gzreg.html">AxReg</mi> $.
$s class AxInf $: <mi href="df-gzinf.html">AxInf</mi> $.
$s class IntgRing $: <mi href="df-irng.html"> IntgRing </mi> $.
$s class cplMetSp $: <mi href="df-cplmet.html"> cplMetSp </mi> $.
$s class HomLimB $: <mi href="df-homlimb.html"> HomLimB </mi> $.
$s class HomLim $: <mi href="df-homlim.html"> HomLim </mi> $.
$s class polyFld $: <mi href="df-plfl.html"> polyFld </mi> $.
$s class splitFld $: <mi href="df-sfl.html"> splitFld </mi> $.
$s class splitFld1 $: <msub href="df-sfl1.html"><mi> splitFld </mi> <mn>1</mn></msub> $.
$s class polySplitLim $: <mi href="df-psl.html"> polySplitLim </mi> $.
$s class t*rec $: <mi href="df-rtrclrec.html">t*rec</mi> $.
$s class numer $: <mi href="df-numer.html">numer</mi> $.
$s class denom $: <mi href="df-denom.html">denom</mi> $.

$( Metamath formal systems $)
$s class mCN $: <mi href="df-mcn.html">mCN</mi> $.
$s class mVR $: <mi href="df-mvar.html">mVR</mi> $.
$s class mType $: <mi href="df-mty.html">mType</mi> $.
$s class mVT $: <mi href="df-mvt.html">mVT</mi> $.
$s class mTC $: <mi href="df-mtc.html">mTC</mi> $.
$s class mAx $: <mi href="df-max.html">mAx</mi> $.
$s class mREx $: <mi href="df-mrex.html">mREx</mi> $.
$s class mEx $: <mi href="df-mex.html">mEx</mi> $.
$s class mDV $: <mi href="df-mdv.html">mDV</mi> $.
$s class mVars $: <mi href="df-mvrs.html">mVars</mi> $.
$s class mRSubst $: <mi href="df-mrsub.html">mRSubst</mi> $.
$s class mSubst $: <mi href="df-msub.html">mSubst</mi> $.
$s class mVH $: <mi href="df-mvh.html">mVH</mi> $.
$s class mPreSt $: <mi href="df-mpst.html">mPreSt</mi> $.
$s class mStRed $: <mi href="df-msr.html">mStRed</mi> $.
$s class mStat $: <mi href="df-msta.html">mStat</mi> $.
$s class mFS $: <mi href="df-mfs.html">mFS</mi> $.
$s class mCls $: <mi href="df-mcls.html">mCls</mi> $.
$s class mPPSt $: <mi href="df-mpps.html">mPPSt</mi> $.
$s class mThm $: <mi href="df-mthm.html">mThm</mi> $.

$s class m0St $: <mi href="df-m0s.html">m0St</mi> $.
$s class mSA $: <mi href="df-msa.html">mSA</mi> $.
$s class mWGFS $: <mi href="df-mwgfs.html">mWGFS</mi> $.
$s class mSyn $: <mi href="df-msy.html">mSyn</mi> $.
$s class mESyn $: <mi href="df-mesy.html">mESyn</mi> $.
$s class mGFS $: <mi href="df-mgfs.html">mGFS</mi> $.
$s class mTree $: <mi href="df-mtree.html">mTree</mi> $.
$s class mST $: <mi href="df-mst.html">mST</mi> $.
$s class mSAX $: <mi href="df-msax.html">mSAX</mi> $.
$s class mUFS $: <mi href="df-mufs.html">mUFS</mi> $.

$s class mUV $: <mi href="df-muv.html">mUV</mi> $.
$s class mVL $: <mi href="df-mvl.html">mVL</mi> $.
$s class mVSubst $: <mi href="df-mvsb.html">mVSubst</mi> $.
$s class mFresh $: <mi href="df-mfsh.html">mFresh</mi> $.
$s class mFRel $: <mi href="df-mfrel.html">mFRel</mi> $.
$s class mEval $: <mi href="df-mevl.html">mEval</mi> $.
$s class mMdl $: <mi href="df-mdl.html">mMdl</mi> $.
$s class mUSyn $: <mi href="df-musyn.html">mUSyn</mi> $.
$s class mGMdl $: <mi href="df-gmdl.html">mGMdl</mi> $.
$s class mItp $: <mi href="df-mitp.html">mItp</mi> $.
$s class mFromItp $: <mi href="df-mfitp.html">mFromItp</mi> $.


$( PseudoMetrics and Uniformities $)
$s class PsMet $: <mi href="df-psmet.html">PsMet</mi> $.
$s class uCn $: <mi href="df-ucn.html">uCn</mi> $.
$s class CnExt $: <mi href="df-cnext.html">CnExt</mi> $.
$s class UnifSt $: <mi href="df-uss.html">UnifSt</mi> $.
$s class unifTop $: <mi href="df-utop.html">unifTop</mi> $.
$s class UnifOn $: <mi href="df-ust.html">UnifOn</mi> $.
$s class UnifSet $: <mi href="df-unif.html">UnifSet</mi> $.
$s class UnifSp $: <mi href="df-unifsp.html">UnifSp</mi> $.
$s class CUnifSp $: <mi href="df-cusp.html">CUnifSp</mi> $.
$s class toUnifSp $: <mi href="df-tus.html">toUnifSp</mi> $.
$s class metUnif $: <mi href="df-metu.html">metUnif</mi> $.
$s class ~Met $: <msub href="df-metid.html"><mo>~</mo> <mi mathvariant="italic">Met</mi></msub> $.
$s class pstoMet $: <mi href="df-pstm.html">pstoMet</mi> $.
$s class HCmp $: <mi href="df-hcmp.html">HCmp</mi> $.


$( Hilbert Spaces $)
$s class ~H $: <mi href="df-hba.html"> &#8459;</mi> $.
$s class 0h $: <msub href="df-h0v.html"><mi>0</mi> <mi>&#x210E;</mi></msub> $. 
$s class +h $: <msub href="h2hva.html"><mo>+</mo> <mi>&#x210E;</mi></msub> $. 
$s class -h $: <msub href="df-hvsub.html"><mo>-</mo> <mi>&#x210E;</mi></msub> $. 
$s class .h $: <msub href="h2hsm.html"><mo>&sdot;</mo> <mi>&#x210E;</mi></msub> $. 
$s class .ih $: <msub href="ax-hfi.html"><mo>&sdot;</mo> <mi>ih</mi></msub> $. 
$s class normh $: <msub href="df-hnorm.html"><mo>norm</mo> <mi>&#x210E;</mi></msub> $. 
$s class -op $: <msub href="df-hodif.html"><mo>-</mo> <mi>op</mi></msub> $. 
$s class +op $: <msub href="df-hosum.html"><mo>+</mo> <mi>op</mi></msub> $. 
$s class .op $: <msub href="df-homul.html"><mo>&middot;</mo> <mi>op</mi></msub> $. 
$s class 0op $: <msub href="df-0o.html"><mi>0</mi> <mi>op</mi></msub> $. 
$s class <_op $: <msub href="df-leop.html"><mi>&le;</mi> <mi>op</mi></msub> $. 
$s class +fn $: <msub href="df-hfsum.html"><mo>+</mo> <mi>fn</mi></msub> $. 
$s class .fn $: <msub href="df-hfmul.html"><mo>&middot;</mo> <mi>fn</mi></msub> $. 
$s class 0hop $: <msub href="df-h0op.html"><mi>0</mi> <mi>hop</mi></msub> $. 
$s class Iop $: <msub href="df-iop.html"><mi>I</mi> <mi>op</mi></msub> $. 
$s class normop $: <msub href="df-nmop.html"><mo>norm</mo> <mi>op</mi></msub> $. 
$s class normfn $: <msub href="df-nmfn.html"><mo>norm</mo> <mi>fn</mi></msub> $. 
$s class adjh $: <msub href="df-adjh.html"><mo>adj</mo> <mi>h</mi></msub> $. 
$s class +H $: <msub href="df-shs.html"><mo>+</mo> <mi>&#8459;</mi></msub> $.
$s class vH $: <msub href="df-chj.html"><mo>&or;</mo> <mi>&#8459;</mi></msub> $.
$s class \/H $: <msub href="df-chsup.html"><mo>&#x22C1;</mo> <mi>&#8459;</mi></msub> $.
$s class 0H $: <msub href="df-ch0.html"><mi>0</mi> <mi>&#8459;</mi></msub> $.
$s class projh $: <msub href="df-pjh.html"><mi>proj</mi> <mi>&#x210E;</mi></msub> $.
$s class C_H $: <msub href="df-cm.html"><mo>&#x1D436;</mo> <mi>&#8459;</mi></msub> $.
$s class CH $: <msub href="df-ch.html"><mo mathvariant="bold">C</mo> <mi>&#8459;</mi></msub> $.
$s class SH $: <msub href="df-sh.html"><mo mathvariant="bold">S</mo> <mi>&#8459;</mi></msub> $.
$s class <oH $: <msub href="df-cv.html"><mo>&#8918;</mo> <mi>&#8459;</mi></msub> $. 
$s class MH $: <msub href="df-md.html"><mo>&#x1D440;</mo> <mi>&#8459;</mi></msub> $. 
$s class MH* $: <msubsup href="df-dmd.html"><mo>&#x1D440;</mo> <mi>&#8459;</mi> <mi>*</mi></msubsup> $. 
$s class _|_ $: <mo href="df-oc.html">&perp;</mo> $.

$( Thierry Arnoux $)

$( Ordered Structures $)
$s class oGrp $: <mi href="df-ogrp.html">oGrp</mi> $.
$s class oField $: <mi href="df-ofld.html">oField</mi> $.
$s class <<< $: <mo href="df-inftm.html">&#x22D8;</mo> $.
$s class Archi $: <mi href="df-archi.html">Archi</mi> $.
$s class oMnd $: <mi href="df-omnd.html">oMnd</mi> $.
$s class oRing $: <mi href="df-orng.html">oRing</mi> $.
$s class SRing $: <mi href="df-srg.html">SRing</mi> $.
$s class SLMod $: <mi href="df-slmod.html">SLMod</mi> $.
$s class sgns $: <msub href="df-sgns.html"><mo>sgn</mo> <mi>s</mi></msub> $.

$( Cannonical embeddings $)
$s class ZRHom $: <mi href="df-zrh.html">&#8484;RHom</mi> $.
$s class ZMod $: <mi href="df-zlm.html">&#8484;Mod</mi> $.
$s class QQHom $: <mi href="df-qqh.html">&Qopf;Hom</mi> $.
$s class RRHom $: <mi href="df-rrh.html">&Ropf;Hom</mi> $.
$s class RR*Hom $: <mi href="df-xrh.html"><msup><mi>&Ropf;</mi> <mo>*</mo></msup>Hom</mi> $.
$s class RRExt $: <mi href="df-rrext.html">&Ropf;Ext</mi> $.

$( Indicator function $)
$s class _Ind $: <mi href="df-ind.html">&#x1D7D9;</mi> $.
$s class ( _Ind ` O ) $: <msub><mi href="df-ind.html">&#x1D7D9;</mi> #O#</msub> $.

$( Topology $)
$s class CovHasRef A $: <mrow><mi href="df-cref.html">CovHasRef</mi> #A#</mrow> $.
$s class Ldlf $: <mi href="df-ldlf.html">Ldlf</mi> $.
$s class Paracomp $: <mi href="df-pcmp.html">Paracomp</mi> $.
$s class ManTop $: <mi href="df-mntop.html">ManTop</mi> $.

$( Number Theory $)
$s class repr $: <mi href="df-repr.html">repr</mi> $.
$s class vts $: <mi href="df-vts.html">vts</mi> $.


$( Measure Theory $)
$s class sigAlgebra $: <mi href="df-siga.html">sigAlgebra</mi> $.
$s class sigaGen $: <mi href="df-sigagen.html">&#x1d6d4;</mi> $. $( Gives a warning, but with &sigma; there is no distinction ` sigma ` $)
$s class BrSiga $: <msub href="df-brsiga.html"><mi>&#x1D505;</mi> <mi>&Ropf;</mi></msub> $.
$s class sX $: <msub href="df-sx.html"><mo>&times;</mo> <mi>s</mi></msub> $.
$s class measures $: <mi href="df-meas.html">measures</mi> $.
$s class Ddelta $: <mi href="df-dde.html">&delta;</mi> $.
$s class ae $: <mi href="df-ae.html">ae</mi> $.
$s class ~ae $: <msub href="df-fae.html"><mo>~</mo><mi>ae</mi></msub> $.
$s wff A ae B $: <mrow>#A# #B#<mi href="df-ae.html">-ae.</mi></mrow> $.
$s wff { x e. A | ph } ae B $: <mrow>#ph# <msub><mrow>#B#<mi href="df-ae.html">-ae.</mi></mrow> <mrow>#x# <mo>&isin;</mo> #A#</mrow></msub></mrow> $.
$s wff R ~ae C $: <msub>#R# <mrow>#C#<mi href="df-fae.html">-ae.</mi></mrow></msub> $.
$s wff A ( R ~ae C ) B $: <mrow>#A# #R# #B# #C#<mi href="df-fae.html">-ae.</mi></mrow> $.
$s class toOMeas $: <mi href="df-oms.html">toOMeas</mi> $.
$s class toCaraSiga $: <mi href="df-carsg.html">toCaraSiga</mi> $.
$s class MblFnM $: <msub href="df-mbfm.html"><mi>MblFn</mi> <mi>&mu;</mi></msub> $.
$s class itgm $: <mi href="df-itgm.html">itgm</mi> $.
$s class sitg $: <mi href="df-sitg.html">sitg</mi> $.
$s class sitm $: <mi href="df-sitm.html">sitm</mi> $.
$s class ( ( A itgm B ) ` F ) $: <mrow><msubsup><mo href="df-itgm.html">&#x222B;</mo> <mi>&mu;</mi> #A#</msubsup> #F# <mo>d</mo>#B#</mrow> $.
$s class ( ( A sitg B ) ` F ) $: <mrow><msubsup><mo href="df-sitg.html">&#x222B;</mo> <mi>&#x2111;</mi> #A#</msubsup> #F# <mo>d</mo>#B#</mrow> $.
$s class dom ( A sitg B ) $: <msubsup><mo href="df-sitg.html">&#x2111;</mo> #B# #A#</msubsup> $.
$s class ( A sitm B ) $: <msubsup><mrow><mo>&vert;</mo><mi>.</mi> <mo>-</mo> <mi>.</mi><mo>&vert;</mo></mrow> #B# #A#</msubsup> $. $( Looks like mfenced does not work with &vert; $)
$s class ( F ( A sitm B ) G ) $: <msubsup><mrow><mo>&vert;</mo>#G# <mo>-</mo> #F#<mo>&vert;</mo></mrow> #B# #A#</msubsup> $. $( Looks like mfenced does not work with &vert; $)
$s class-o ( F ( A sitm B ) G ) $: <msubsup><mrow><mo>&vert;</mo>#G# <mo>-</mo> #F#<mo>&vert;</mo></mrow> #B# #A#</msubsup> $. $( Looks like mfenced does not work with &vert; $)
$s class Prob $: <mi href="df-prob.html">Prob</mi> $.
$s class cprob $: <mi href="df-cndprob.html">cProb</mi> $.
$s class rRndVar $: <msub href="df-rrv.html"><mi>RndVar</mi> <mi>&Ropf;</mi></msub> $.
$s class oRVC R $: <mrow> <msub><mo href="df-orvc.html">&compfn;</mo> <mi>RV/c</mi></msub> <mo>&ApplyFunction;</mo> #R# </mrow> $.
$s class ( F oRVC R A ) $: <mfenced><mrow>#F# <msub>#R# <mi href="df-orvc.html">RV/c</mi></msub> #A#</mrow></mfenced> $.
$s class-o ( F oRVC R A ) $: <mrow>#F# <msub>#R# <mi href="df-orvc.html">RV/c</mi></msub> #A#</mrow> $.


$( p-adic number fields $)
$s class ZRing $: <mi href="df-zrng.html">&Zopf;Ring</mi> $.
$s class GF $: <mi href="df-gf.html"> GF </mi> $.
$s class ~Qp $: <msub href="df-eqp.html"><mo>~</mo><msub><mi>&Qopf;</mi><mi>p</mi></msub></msub> $.
$s class /Qp $: <msub href="df-rqp.html"><mo>/</mo><msub><mi>&Qopf;</mi><mi>p</mi></msub></msub> $.
$s class Qp $: <msub href="df-qp.html"><mi>&Qopf;</mi><mi>p</mi></msub> $.
$s class QpOLD $: <msub href="df-qpOLD.html"><mi>&Qopf;OLD</mi><mi>p</mi></msub> $.
$s class Zp $: <msub href="df-zp.html"><mi>&Zopf;</mi><mi>p</mi></msub> $.
$s class _Qp $: <mover href="df-qpa.html"><msub><mi>&Qopf;</mi><mi>p</mi></msub> <mo>&oline;</mo></mover> $.
$s class Cp $: <msub href="df-cp.html"><mi>&Copf;</mi><mi>p</mi></msub> $.


$( Graph Theory $)
$s class UMGraph $: <mi href="df-umgr.html">UMGraph</mi> $.
$s class UHGraph $: <mi href="df-uhgr.html">UHGraph</mi> $.
$s class USHGraph $: <mi href="df-ushgr.html">USHGraph</mi> $.
$s class USGraph $: <mi href="df-usgr.html">USGraph</mi> $.
$s class SubGraph $: <mi href="df-subgr.html">SubGraph</mi> $.
$s class NeighbVtx $: <mi href="df-nbgr.html">NeighbVtx</mi> $.
$s class ComplGraph $: <mi href="df-cplgr.html">ComplGraph</mi> $.
$s class ComplUSGraph $: <mi href="df-cusgr.html">ComplUSGraph</mi> $.
$s class UnivVtx $: <mi href="df-uvtx.html">UnivVtx</mi> $.
$s class .ef $: <mi href="df-edgf.html"> ef </mi> $.
$s class Vtx $: <mi href="df-vtx.html"> Vtx </mi> $.
$s class iEdg $: <mi href="df-iedg.html"> iEdg </mi> $.
$s class Edg $: <mi href="df-edg.html"> Edg </mi> $.
$s class UPGraph $: <mi href="df-upgr.html"> UPGraph </mi> $.
$s class USPGraph $: <mi href="df-ushgr.html"> USHGraph </mi> $.
$s class FinUSGraph $: <mi href="df-fusg.html"> FinUSGraph </mi> $.
$s class EulerPaths $: <mi href="df-eupth.html"> EulerPaths </mi> $.
$s class VtxDeg $: <mi href="df-vtxdg.html"> VtxDeg </mi> $.
$s class Walks $: <mi href="df-wlk.html">Walks</mi> $.
$s class Trails $: <mi href="df-trls.html">Trails</mi> $.
$s class TrailsOn $: <mi href="df-trlson.html">TrailsOn</mi> $.
$s class Paths $: <mi href="df-pth.html">Paths</mi> $.
$s class SPaths $: <mi href="df-spth.html">SPaths</mi> $.
$s class PathsOn $: <mi href="df-pthson.html">PathsOn</mi> $.
$s class SPathsOn $: <mi href="df-spthson.html">SPathsOn</mi> $.
$s class Circuits $: <mi href="df-crct.html">Circuits</mi> $.
$s class Cycles $: <mi href="df-cycl.html">Cycles</mi> $.
$s class ConnGraph $: <mi href="df-conngr.html">ConnGraph</mi> $.
$s class WWalks $: <mi href="df-wwlk.html">WWalks</mi> $.
$s class WWalksN $: <mi href="df-wwlkn.html">WWalksN</mi> $.
$s class WWalksNOn $: <mi href="df-wwlksnon.html">WWalksNOn</mi> $.
$s class WSPathsN $: <mi href="df-wspthsn.html">WSPathsN</mi> $.
$s class WSPathsNOn $: <mi href="df-wspthsnon.html">WSPathsNOn</mi> $.
$s class RegGraph $: <mi href="df-rgr.html">RegGraph</mi> $.
$s class RegUSGraph $: <mi href="df-rusgr.html">RegUSGraph</mi> $.
$s class ClWalks $: <mi href="df-clwlk.html">ClWalks</mi> $.
$s class ClWWalks $: <mi href="df-clwwlk.html">ClWWalks</mi> $.
$s class ClWWalksN $: <mi href="df-clwwlkn.html">ClWWalksN</mi> $.

$s class seqstr $: <msub href="df-sseq.html"><mi>seq</mi> <mo>str</mo></msub> $.
$s class Fibci $: <mi href="df-fibci.html">Fibci</mi> $.



$s class CVecOLD $: <msub href="df-vc.html"><mo>CVec</mo> <mi>OLD</mi></msub> $.
$s class .sOLD $: <msub href="df-sm.html"><mo>&sdot;</mo> <mi>&#x1D460;OLD</mi></msub> $.
$s class .iOLD $: <msub href="df-dip.html"><mo>&sdot;</mo> <mi>&#x1D456;OLD</mi></msub> $.
$s class normOpOLD $: <msub href="df-nmoo.html"><mo>normOp</mo> <mi>OLD</mi></msub> $.
$s class CPreHilOLD $: <msub href="df-ph.html"><mo>CPreHil</mo> <mi>OLD</mi></msub> $.
$s class CHilOLD $: <msub href="df-hlo.html"><mo>CHil</mo> <mi>OLD</mi></msub> $.

$( M L $)
$s class ( A ^^ B ) $: <mrow> #A# <mo href="df-finxp.html">&uarr;&uarr;</mo> #B# </mrow> $.


$( Wolf Lammen $)
$s wff x wl-el A $: <mrow> #A# <mo href="ax-wl-8cl.html">&isin;</mo> #B# </mrow> $.
$s wff x wl-el2 A $: <mrow> #A# <mo href="df-wl-clelv2.html">&isin;</mo> #B# </mrow> $.


$( Removed as part of FL'mathbox

$s class <> $: <mi>&#9671;</mi> $.
$s class [.] $: <mi>&#9723;</mi> $.
$s class () $: <mi>&#9675;</mi> $.
$s class until $: <mi> until </mi> $.
$s class pr $: <mi href="df-pro.html"> pr </mi> $.
$s class prj $: <mi href="df-prj.html"> prj </mi> $.
$s class cset $: <mi href="df-cst.html">cset</mi> $.
$s class LatAlg $: <mi href="df-latalg.html">LatAlg</mi> $.
$s class cur1 $: <mi href="df-cur1.html">cur1</mi> $.
$s class cur2 $: <mi href="df-cur2.html">cur2</mi> $.
$s class OrHom $: <mi href="df-orhom.html"> OrHom </mi> $.
$s class OrIso $: <mi href="df-oriso.html"> OrIso </mi> $.
$s class mxl $: <mi href="df-mxl.html">mxl</mi> $.
$s class mnl $: <mi href="df-mnl.html">mnl</mi> $.
$s class ub $: <mi href="df-ub.html"> ub </mi> $.
$s class lb $: <mi href="df-lb.html">lb</mi> $.
$s class PresetRel $: <mi href="df-prs.html">PresetRel</mi> $.
$s class ge $: <mi href="df-ge.html">ge</mi> $.
$s class leR $: <mi href="df-ler.html">leR</mi> $.
$s class AntiDir $: <mi href="df-antidir.html">AntiDir</mi> $.
$s class BndLat $: <mi href="df-bnlat.html">BndLat</mi> $.
$s class Com1 $: <mi href="df-com1.html">Com1</mi> $.
$s class SubSemiGrp $: <mi href="df-subsmg.html">SubSemiGrp</mi> $.
$s class subSemiGrpGen $: <mi href="df-sggen.html">subSemiGrpGen</mi> $.
$s class SemiGrpHom $: <mi href="df-gsmhom.html">SemiGrpHom</mi> $.
$s class FreeSemiGrp $: <mi href="df-frsmgrp.html">FreeSemiGrp</mi> $.
$s class Tofld $: <mi href="df-tofld.html"> Tofld </mi> $.
$s class zeroDiv $: <mi href="df-zd.html"> zeroDiv </mi> $.
$s class IdlNEW $: <mi href="df-idlNEW.html">IdlNEW</mi> $.
$s class Action $: <mi href="df-act.html">Action</mi> $.
$s class Vec $: <mi href="df-vec.html"> Vec </mi> $.
$s class SubVec $: <mi href="df-svs.html">SubVec</mi> $.
$s class RVec $: <mi href="df-vr.html"> RVec </mi> $.
$s class RAffSp $: <mi href="df-raffsp.html"> RAffSp </mi> $.
$s class topX $: <mi href="df-prtop.html"> topX </mi> $.
$s class fLimfrs $: <mi href="df-flimfrs.html"> fLimfrs </mi> $.
$s class IsolatedPt $: <mi href="df-islpt.html">IsolatedPt</mi> $.
$s class opfn $: <mi href="df-opfn.html"> opfn </mi> $.
$s class TopFld $: <mi href="df-topfld.html"> TopFld </mi> $.
$s class sup_ $: <mi> sup_ </mi> $.
$s class inf_ $: <mi> inf_ </mi> $.
$s class Frf $: <mi href="df-frf.html">Frf</mi> $.
$s class +cv $: <mi href="df-addcv.html">+cv</mi> $.
$s class 0cv $: <mi href="df-nullcv.html">0cv</mi> $.
$s class Intvl $: <mi href="df-intvl.html">Intvl</mi> $.
$s class der $: <mi href="df-der.html">der</mi> $.
$s class Dgra $: <mi href="df-mgra.html"> Dgra </mi> $.
$s class Alg $: <mi href="df-alg.html"> Alg </mi> $.
$s class Ded $: <mi href="df-ded.html"> Ded </mi> $.
$s class hom $: <mi href="df-homOLD.html"> hom </mi> $.
$s class Epic $: <mi href="df-epiOLD.html">Epic</mi> $.
$s class Isofunc $: <mi href="df-isof.html"> Isofunc </mi> $.
$s class SubCat $: <mi href="df-subcat.html"> SubCat </mi> $.
$s class InitObj $: <mi href="df-inob.html"> InitObj </mi> $.
$s class TermObj $: <mi href="df-termob.html"> TermObj </mi> $.
$s class Source $: <mi href="df-source.html"> Source </mi> $.
$s class Sink $: <mi href="df-sink.html"> Sink </mi> $.
$s class Natural $: <mi href="df-natur.html"> Natural </mi> $.
$s class LimCat $: <mi href="df-limcat.html"> LimCat </mi> $.
$s class ProdObj $: <mi href="df-prodobj.html"> ProdObj </mi> $.
$s class tar $: <mi href="df-tar.html">tar</mi> $.
$s class tr $: <mi href="df-trcls.html">tr</mi> $.
$s class line $: <mi href="df-li.html">line</mi> $.
$s class seg $: <mi href="df-seg2.html">seg</mi> $.
$s class Kleene $: <mi href="df-kle.html">Kleene</mi> $.
$s class Words $: <mi href="df-words.html"> Words </mi> $.
$s class IndCls $: <mi href="df-indcls.html"> IndCls </mi> $.
$s class Grammar $: <mi href="df-grm.html">Grammar</mi> $.
$s class sym $: <mi href="df-sym.html">sym</mi> $.
$s class prdct $: <mi href="df-prodct.html">prdct</mi> $.
$s class conc $: <mi href="df-conc.html"> conc </mi> $.
$s class Prop $: <mi href="df-prop.html">Prop</mi> $.
$s class derv $: <mi href="df-derv.html">derv</mi> $.
$s class PPoints $: <mi href="df-points.html">PPoints</mi> $.
$s class PLines $: <mi href="df-plines.html">PLines</mi> $.
$s class Ig $: <mi href="df-ig2.html">Ig</mi> $.
$s class coln $: <mi href="df-col.html">coln</mi> $.
$s class con $: <mi href="df-con2.html">con</mi> $.
$s class Ibg $: <mi href="df-ibg2.html">Ibg</mi> $.
$s class btw $: <mi href="df-btw.html">btw</mi> $.
$s class Segments $: <mi href="df-Seg.html">Segments</mi> $.
$s class ray $: <mi href="df-ray2.html">ray</mi> $.
$s class convex $: <mi href="df-cnvx.html">convex</mi> $.
$s class Ibcg $: <mi href="df-ibcg.html">Ibcg</mi> $.
$s class angc $: <mi href="df-angc.html">angc</mi> $.
$s class segc $: <mi href="df-segc.html">segc</mi> $.
$s class slices $: <mi href="df-slices.html">slices</mi> $.
$s class Cut $: <mi href="df-Cut.html">Cut</mi> $.
$s class Neug $: <mi href="df-neug.html">Neug</mi> $.
$s class Circle $: <mi href="df-crcl.html">Circle</mi> $.
$s class angle $: <mi href="df-angle.html">angle</mi> $.
$s class triangle $: <mi href="df-triangle.html">triangle</mi> $.
$s class dWords $: <mi href="df-dwords.html">dWords</mi> $.
$s class ss $: <mi href="df-sside.html">ss</mi> $.
$s class trcng $: <mi href="df-trcng.html">trcng</mi> $.
$s class Halfplane $: <mi href="df-halfplane.html">Halfplane</mi> $.
$s class angtrg $: <mi href="df-angtrg.html">angtrg</mi> $.
$s class segtrg $: <mi href="df-segtrg.html">segtrg</mi> $.
$s class CatOLD $: <msub href="df-catOLD.html"><mo>Cat</mo> <mi>OLD</mi></msub> $.
$s class SetCatOLD $: <msub href="df-catset.html"><mo>SetCat</mo> <mi>OLD</mi></msub> $.
$s class MonoOLD $: <msub href="df-monOLD.html"><mo>Mono</mo> <mi>OLD</mi></msub> $.
$s class IsoOLD $: <msub href="df-isoc.html"><mo>Iso</mo> <mi>OLD</mi></msub> $.
$s class cinvOLD $: <msub href="df-cinv.html"><mo>cinv</mo> <mi>OLD</mi></msub> $.
$s class FuncOLD $: <msub href="df-funcOLD.html"><mo>Func</mo> <mi>OLD</mi></msub> $.
$s class MorphismSetCat $: <msub href="df-morcatset.html"><mo>Morphism</mo> <mi>SetCat</mi></msub> $.
$s class domSetCat $: <msub href="df-domcatset.html"><mo>dom</mo> <mi>SetCat</mi></msub> $.
$s class graphSetCat $: <msub href="df-graphcatset.html"><mo>graph</mo> <mi>SetCat</mi></msub> $.
$s class codSetCat $: <msub href="df-codcatset.html"><mo>cod</mo> <mi>SetCat</mi></msub> $.
$s class IdSetCat $: <msub href="df-idcatset.html"><mo>Id</mo> <mi>SetCat</mi></msub> $.
$s class roSetCat $: <msub href="df-rocatset.html"><mo>ro</mo> <mi>SetCat</mi></msub> $.

$s class dom_ $: <munder href="df-dom_.html"><mo>dom</mo> <mo>&#x5F;</mo></munder> $. 
$s class cod_ $: <munder href="df-cod_.html"><mo>cod</mo> <mo>&#x5F;</mo></munder> $. 
$s class id_ $: <munder href="df-id_.html"><mo>id</mo> <mo>&#x5F;</mo></munder> $. 
$s class o_ $: <munder href="df-cmpa.html"><mo>o</mo> <mo>&#x5F;</mo></munder> $. 

$s class ^md $: <msub href="df-expsg.html"><mo>&uarr;</mo> <mi>md</mi></msub> $.
$s class +m $: <msub href="df-amat.html"><mo>+</mo> <mi>&#x1D45A;</mi></msub> $. 
$s class .m $: <msub href="df-smat.html"><mo>&sdot;</mo> <mi>&#x1D45A;</mi></msub> $. 
$s class xm $: <msub href="df-mmat.html"><mo>&times;</mo> <mi>&#x1D45A;</mi></msub> $.

End of FL's mathbox removed
$)

$( Constant classes with subscript rules $)
$s class PwSer1 $: <msub href="df-psr1.html"><mi>PwSer</mi> <mn>1</mn></msub> $.
$s class var1 $: <msub href="df-vr1.html"><mi>var</mi> <mn>1</mn></msub> $.
$s class Poly1 $: <msub href="df-ply1.html"><mi>Poly</mi> <mn>1</mn></msub> $.
$s class evalSub1 $: <msub href="df-evls1.html"><mi>evalSub</mi> <mn>1</mn></msub> $.
$s class eval1 $: <msub href="df-evl1.html"><mi>eval</mi> <mn>1</mn></msub> $.
$s class deg1 $: <msub href="df-deg1.html"><mi>deg</mi> <mn>1</mn></msub> $.
$s class coe1 $: <msub href="df-coe1.html"><mi>coe</mi> <mn>1</mn></msub> $.
$s class toPoly1 $: <msub href="df-toply1.html"><mi>toPoly</mi> <mn>1</mn></msub> $.
$s class *p $: <msub href="df-pco.html"><mo>*</mo> <mi>&#x1D45D;</mi></msub> $.
$s class Om1 $: <msub href="df-om1.html"><mo>&Omega;</mo> <mn>1</mn></msub> $.
$s class OmN $: <msub href="df-omn.html"><mo>&Omega;</mo> <mn>&#x1D45B;</mn></msub> $.
$s class pi1 $: <msub href="df-pi1.html"><mo>&pi;</mo> <mn>1</mn></msub> $.
$s class piN $: <msub href="df-pin.html"><mo>&pi;</mo> <mn>&#x1D45B;</mn></msub> $.
$s class .if $: <msub href="df-ipf.html"><mo>&sdot;</mo> <mi>if</mi></msub> $.
$s class gcdOLD ( A , B ) $: <mrow><msub><mo>gcd</mo> <mi>OLD</mi></msub> <mfenced>#A# #B#</mfenced></mrow> $.

$s class Monic1p $: <msub href="df-mon1.html"><mo>Monic</mo> <mi>1p</mi></msub> $.
$s class Unic1p $: <msub href="df-uc1p.html"><mo>Unic</mo> <mi>1p</mi></msub> $.
$s class quot1p $: <msub href="df-q1p.html"><mo>quot</mo> <mi>1p</mi></msub> $.
$s class rem1p $: <msub href="df-r1p.html"><mo>rem</mo> <mi>1p</mi></msub> $.
$s class idlGen1p $: <msub href="df-ig1p.html"><mo>idlGen</mo> <mi>1p</mi></msub> $.
$s class GF_oo $: <msub href="df-gfoo.html"><mi>GF</mi> <mi>&infin;</mi></msub> $.

$s class ^ko $: <msub href="df-xko.html"><mi>^</mi> <mi>ko</mi></msub> $.
$s class C^n $: <msup href="df-cpn.html"><mi>C</mi> <mi>n</mi></msup> $.
$s class Dn $: <msup href="df-dvn.html"><mi>D</mi> <mi>n</mi></msup> $.
$s class Xp $: <msup href="df-idp.html"><mi>X</mi> <mi>p</mi></msup> $.
$s class ~= $: <mo href="df-hmph.html">&simeq;</mo> $.
$s class ~=ph $: <msub href="df-phtpc.html"><mo>&simeq;</mo> <mi>ph</mi></msub> $.

$s class /L $: <msub href="df-lgs.html"><mo>/</mo> <mi>L</mi></msub> $. 
$s class /g $: <msub href="df-gdiv.html"><mo>/</mo> <mi>g</mi></msub> $. 
$s class ^c $: <msub href="df-cxp.html"><mo>&uarr;</mo> <mi>c</mi></msub> $. 
$s class +v $: <msub href="df-va.html"><mo>+</mo> <mi>v</mi></msub> $. 
$s class -v $: <msub href="df-vs.html"><mo>-</mo> <mi>v</mi></msub> $. 
$s class .v $: <msub href="df-mulv.html"><mo>&sdot;</mo> <mi>v</mi></msub> $. 
$s class 0vec $: <msub href="df-0v.html"><mi>0</mi> <mi>vec</mi></msub> $. 
$s class normCV $: <msub href="df-nmcv.html"><mo>norm</mo> <mo>CV</mo></msub> $. 

$( Goedel $)
$s class e.g $: <msub href="df-goel.html"><mo>&isin;</mo> <mi>&#x1D454;</mi></msub> $.
$s class |g $: <msub href="df-gona.html"><mo>&#8892;</mo> <mi>&#x1D454;</mi></msub> $.
$s class A.g A B $: <mfenced open="[" close="]" separators=""><msub><mo>&forall;</mo> <mi>&#x1D454;</mi></msub> #A# #B#</mfenced> $.
$s class E.g A B $: <mfenced open="[" close="]" separators=""><msub><mo>&exist;</mo> <mi>&#x1D454;</mi></msub> #A# #B#</mfenced> $.
$s class -.g A $: <mfenced open="[" close="]" separators=""><msub><mo>&not;</mo> <mi>&#x1D454;</mi></msub> #A#</mfenced> $.
$s class =g $: <msub href="df-goeq.html"><mo>=</mo> <mi>&#x1D454;</mi></msub> $.
$s class /\g $: <msub href="df-goan.html"><mo>&and;</mo> <mi>&#x1D454;</mi></msub> $.
$s class \/g $: <msub href="df-goor.html"><mo>&or;</mo> <mi>&#x1D454;</mi></msub> $.
$s class ->g $: <msub href="df-goim.html"><mo>&rarr;</mo> <mi>&#x1D454;</mi></msub> $.
$s class <->g $: <msub href="df-gobi.html"><mo>&harr;</mo> <mi>&#x1D454;</mi></msub> $.
$s class Fmla $: <mi href="df-fmla.html">Fmla</mi> $.
$s class |= $: <mo href="df-prv.html">&#8871;</mo> $.
$s class Sat $: <mi href="df-sat.html">Sat</mi> $.
$s class SatE $: <msub href="df-sate.html"><mi>Sat</mi> <mi>&isin;</mi></msub> $.
$s class ZF $: <mi mathvariant="bold" href="df-gzf.html">ZF</mi> $.


$( Scott Fenton $)
$s class FallFac $: <mo href="df-fallfac.html">FallFac</mo> $. $( With dots: <msup><mi>.</mi> <munder><mi>.</mi> <mo>&#x5F;</mo></munder></msup> $)
$s class RiseFac $: <mo href="df-risefac.html">RiseFac</mo> $. $( With dots: <msup><mi>.</mi> <mover><mi>.</mi> <mo>&oline;</mo></mover></msup> $)
$s class ( A FallFac B ) $: <mfenced><msup>#A# <munder>#B# <mo>&#x5F;</mo></munder></msup></mfenced> $.
$s class ( A RiseFac B ) $: <mfenced><msup>#A# <mover>#B# <mo>&oline;</mo></mover></msup></mfenced> $.
$s class-o ( A FallFac B ) $: <msup>#A# <munder>#B# <mo>&#x5F;</mo></munder></msup> $.
$s class-o ( A RiseFac B ) $: <msup>#A# <mover>#B# <mo>&oline;</mo></mover></msup> $.
$s class Pred ( R , A , B ) $: <mrow> <mo href="df-pred.html">Pred</mo> <mfenced>#R# #A# #B#</mfenced></mrow> $.
$s class TrPred ( R , A , B ) $: <mrow> <mo href="df-trpred.html">TrPred</mo> <mfenced>#R# #A# #B#</mfenced></mrow> $.
$s class EE $: <mi href="df-ee.html"> &#x1D53C; </mi> $.
$s class Btwn $: <mi href="df-btwn.html"> Btwn </mi> $.
$s class Cgr $: <mi href="df-cgr.html">Cgr</mi> $.
$s class OuterFiveSeg $: <mi href="df-ofs.html"> OuterFiveSeg </mi> $.
$s class TransportTo $: <mi href="df-transport.html">TransportTo</mi> $.
$s class InnerFiveSeg $: <mi href="df-ifs.html"> InnerFiveSeg </mi> $.
$s class Cgr3 $: <mi href="df-cgr3.html">Cgr3</mi> $.
$s class Colinear $: <mi href="df-colinear.html"> Colinear </mi> $.
$s class FiveSeg $: <mi href="df-fs.html"> FiveSeg </mi> $.
$s class Seg<_ $: <msub href="df-segle.html"><mi>Seg</mi> <mo>&le;</mo></msub> $.
$s class OutsideOf $: <mi href="df-outsideof.html">OutsideOf</mi> $.
$s class Line $: <mi href="df-line2.html">Line</mi> $.
$s class LinesEE $: <mi href="df-lines2.html">LinesEE</mi> $.
$s class Ray $: <mi href="df-ray.html">Ray</mi> $.
$s class BernPoly $: <mi href="df-bpoly.html"> BernPoly </mi> $.
$s class Hf $: <mi href="df-hf.html"> Hf </mi> $.

$( Founded recursion $)
$s class frecs ( R , O , P ) $: <mrow> <mi href="df-frecs.html">frecs</mi> <mo>&ApplyFunction;</mo> <mfenced> #R# #O# #P# </mfenced> </mrow> $. $( Removed stretchy="false" $)

$( Surreal Numbers $)
$s class No $: <mi href="df-no.html">No</mi> $.
$s class <s $: <msub href="df-slt.html"><mo>&lt;</mo> <mi>s</mi></msub> $.
$s class <_s $: <msub href="df-sle.html"><mo>&le;</mo> <mi>s</mi></msub> $.
$s class <<s $: <msub href="df-sslt.html"><mo>&#x226A;</mo> <mi>s</mi></msub> $.
$s class |s $: <msub href="df-scut.html"><mo>|</mo> <mi>s</mi></msub> $.
$s class bday $: <mi href="df-bday.html">bday</mi> $.
$s class _M $: <mi href="df-made.html">M</mi> $.
$s class _Old $: <mi href="df-old.html">Old</mi> $.
$s class _N $: <mi href="df-new.html">N</mi> $.
$s class _L $: <mi href="df-left.html">L</mi> $.
$s class _R $: <mi href="df-right.html">R</mi> $.

$s class pprod ( A , B ) $: <mrow> <mo>pprod</mo> <mfenced>#A# #B#</mfenced></mrow> $.
$s class << A , B >> $: <mfenced href="df-altop" open="&#10218;" close="&#10219;">#A# #B#</mfenced> $.
$s class ( A XX. B ) $: <mfenced><mrow>#A# <mi href="df-altxp"> &times;&times; </mi> #B#</mrow></mfenced> $.
$s class ( A /_\ B ) $: <mfenced><mrow>#A# <mi href="df-symdif"> &#x2206; </mi> #B#</mrow></mfenced> $.
$s class _/_\ $: <mi href="df-fwddif.html">&#x25b3;</mi> $.
$s class _/_\^n $: <msup><mi href="df-fwddifn.html">&#x25b3;</mi><mi>n</mi></msup> $.
$s class ( A (x) B ) $: <mfenced><mrow>#A# <mi href="df-txp"> &otimes; </mi> #B#</mrow></mfenced> $.
$( $s class (+) $: <mi> &#x2295; </mi> $. $)

$s class SSet $: <mi href="df-sset.html">&#x1D5B2;&#x1D5B2;&#x1D5BE;&#x1D5CD;</mi> $.
$s class Trans $: <mi href="df-trans.html">&#x1D5B3;&#x1D5CB;&#x1D5BA;&#x1D5C7;&#x1D5CC;</mi> $.
$s class Bigcup $: <mi href="df-bigcup.html">&#x1D5A1;&#x1D5C2;&#x1D5C0;&#x1D5BC;&#x1D5CE;&#x1D5C9;</mi> $.
$s class Fix A $: <mrow><mi href="df-fix.html">&#x1D5A5;&#x1D5C2;&#x1D5D1;</mi> #A#</mrow> $.
$s class Limits $: <mi href="df-limits.html">&#x1D5AB;&#x1D5C2;&#x1D5C6;&#x1D5C2;&#x1D5CD;&#x1D5CC;</mi> $.
$s class Funs $: <mi href="df-funs.html">&#x1D5A5;&#x1D5CE;&#x1D5C7;&#x1D5CC;</mi> $.
$s class Singleton $:  <mi>&#x1D5B2;&#x1D5C2;&#x1D5C7;&#x1D5C0;&#x1D5C5;&#x1D5BE;&#x1D5CD;&#x1D5C8;&#x1D5C7;</mi> $.
$s class Singletons $: <mi href="df-singles.html">&#x1D5B2;&#x1D5C2;&#x1D5C7;&#x1D5C0;&#x1D5C5;&#x1D5BE;&#x1D5CD;&#x1D5C8;&#x1D5C7;&#x1D5CC;</mi> $.
$s class Image A $: <mrow><mi href="df-image.html">&#x1D5A8;&#x1D5C6;&#x1D5BA;&#x1D5C0;&#x1D5BE;</mi> #A#</mrow> $.
$s class Cart $: <mi href="df-cart.html">&#x1D5A2;&#x1D5BA;&#x1D5CB;&#x1D5CD;</mi> $.
$s class Img $: <mi href="df-img.html">&#x1D5A8;&#x1D5C6;&#x1D5C0;</mi> $.
$s class Domain $: <mi href="df-domain.html">&#x1D5A3;&#x1D5C8;&#x1D5C6;&#x1D5BA;&#x1D5C2;&#x1D5C7;</mi> $.
$s class Range $: <mi href="df-range.html">&#x1D5B1;&#x1D5BA;&#x1D5C7;&#x1D5C0;&#x1D5BE;</mi> $.
$s class Apply $: <mi href="df-apply.html">&#x1D5A0;&#x1D5C9;&#x1D5C9;&#x1D5C5;&#x1D5D2;</mi> $.
$s class Cup $: <mi href="df-cup.html">&#x1D5A2;&#x1D5CE;&#x1D5C9;</mi> $.
$s class Cap $: <mi href="df-cap.html">&#x1D5A2;&#x1D5BA;&#x1D5C9;</mi> $.
$s class Succ $: <mi href="df-succf.html">&#x1D5B2;&#x1D5CE;&#x1D5BC;&#x1D5BC;</mi> $.
$s class Restrict $: <mi href="df-restrict.html">&#x1D5B1;&#x1D5BE;&#x1D5CC;&#x1D5CD;&#x1D5CB;&#x1D5C2;&#x1D5BC;&#x1D5CD;</mi> $.
$s class Funpart F $: <mrow><mi href="df-funpart.html">&#x1D5A5;&#x1D5CE;&#x1D5C7;&#x1D5AF;&#x1D5BA;&#x1D5CB;&#x1D5CD;</mi> #F#</mrow> $.
$s class FullFun F $: <mrow><mi href="df-fullfun.html">&#x1D5A5;&#x1D5CE;&#x1D5C5;&#x1D5C5;&#x1D5A5;&#x1D5CE;&#x1D5C7;</mi> #F#</mrow> $.
$s class UB A $: <mrow><mi href="df-ub.html">UB</mi> #A# </mrow> $.
$s class LB A $: <mrow><mi href="df-lb.html">LB</mi> #A# </mrow> $.
$s class wsuc ( R , O , P ) $: <mrow> <mo href="df-wsuc.html">wsuc</mo> <mfenced>#R# #O# #P#</mfenced></mrow> $.
$s class WLim ( R , O ) $: <mrow> <mo href="df-wlim.html">WLim</mo> <mfenced>#R# #O#</mfenced></mrow> $.

$s class _|_P $: <msub href="df-polarityN.html"><mo>&perp;</mo> <mi>&#x1D443;</mi></msub> $. 
$s class +P $: <msub href="df-padd.html"><mo>+</mo> <mi>&#x1D443;</mi></msub> $. 

$s class ^r $: <msub href="df-relexp.html"><mo>&uarr;</mo> <mi>r</mi></msub> $.


$( Jeff Madsen $)
$s class Fne $: <mi href="df-fne.html">Fne</mi> $.
$s class Ref $: <mi href="df-ref.html">Ref</mi> $.
$s class PtFin $: <mi href="df-ptfin.html">PtFin</mi> $.
$s class LocFin $: <mi href="df-locfin.html">LocFin</mi> $.
$s class TotBnd $: <mi href="df-totbnd.html">TotBnd</mi> $.
$s class Bnd $: <mi href="df-bnd.html">Bnd</mi> $.
$s class Ismty $: <mi href="df-ismty.html"> Ismty </mi> $.
$s class Rn $: <msup href="df-rrn.html"><mi>&Ropf;</mi> <mi>n</mi></msup> $.
$s class RngHom $: <mi href="df-rngohom.html"> RngHom </mi> $.
$s class RngIso $: <mi href="df-rngoiso.html"> RngIso </mi> $.
$s class ~=R $: <msub href="df-risc.html"><mo>&#8771;</mo> <mi>&#x1D45F;</mi></msub> $.
$s class CRingOps $: <mi href="df-crngo.html">CRingOps</mi> $.
$s class Idl $: <mi href="df-idl.html">Idl</mi> $.
$s class PrIdl $: <mi href="df-pridl.html">PrIdl</mi> $.
$s class MaxIdl $: <mi href="df-maxidl.html">MaxIdl</mi> $.
$s class PrRing $: <mi href="df-prrngo.html">PrRing</mi> $.
$s class Dmn $: <mi href="df-dmn.html">Dmn</mi> $.
$s class IdlGen $: <mi href="df-igen.html">IdlGen</mi> $.

$( Rodolfo Medina $)
$s wff Prt A $: <mrow><mi href="df-prt.html">Prt</mi> #A# </mrow> $.

$( Stefan O'Rear $)
$s class NoeACS $: <mi href="df-nacs.html">NoeACS</mi> $.
$s class mzPolyCld $: <mi href="df-mzpcl.html">mzPolyCld</mi> $.
$s class mzPoly $: <mi href="df-mzp.html">mzPoly</mi> $.
$s class Dioph $: <mi href="df-dioph.html">Dioph</mi> $.

$s class []NN $: <msub href="df-squarenn.html"><mi>&#x25FB;</mi> <mi>&Nopf;</mi></msub> $.
$s class Pell1QR $: <mi href="df-pell1qr.html">Pell1QR</mi> $.
$s class Pell14QR $: <mi href="df-pell14qr.html">Pell14QR</mi> $.
$s class Pell1234QR $: <mi href="df-pell1234qr.html">Pell1234QR</mi> $.
$s class PellFund $: <mi href="df-pellfund.html">PellFund</mi> $.
$s class rmX $: <msub href="df-rmx.html"><mo>X</mo> <mi>rm</mi></msub> $. 
$s class rmY $: <msub href="df-rmy.html"><mo>Y</mo> <mi>rm</mi></msub> $. 
$s class LFinGen $: <mi href="df-lfig.html">LFinGen</mi> $.
$s class LNoeM $: <mi href="df-lnm.html">LNoeM</mi> $.
$s class (+)m $: <msub href="df-dsmm.html"><mo>&#x2295;</mo> <mi>m</mi></msub> $.
$s class freeLMod $: <mi href="df-frlm.html"> freeLMod </mi> $.
$s class unitVec $: <mi href="df-uvc.html"> unitVec </mi> $.
$s class LIndF $: <mi href="df-lindf.html"> LIndF </mi> $.
$s class LIndS $: <mi href="df-linds.html">LIndS</mi> $.
$s class LNoeR $: <mi href="df-lnr.html">LNoeR</mi> $.
$s class ldgIdlSeq $: <mi href="df-ldgis.html">ldgIdlSeq</mi> $.
$s class Monic $: <mi href="df-mnc.html"> Monic </mi> $.
$s class Poly< $: <msub href="df-plylt.html"><mi>Poly</mi> <mo>&lt;</mo></msub> $.
$s class degAA $: <msub href="df-dgraa.html"><mi>deg</mi> <mi>&Aopf;</mi></msub> $.
$s class minPolyAA $: <msub href="df-mpaa.html"><mi>minPoly</mi> <mi>&Aopf;</mi></msub> $.
$s class _ZZ $: <mover href="df-za.html"><mi>&Zopf;</mi> <mo>&oline;</mo></mover> $.
$s class IntgOver $: <mi href="df-itgo.html">IntgOver</mi> $.
$s class pmTrsp $: <mi href="df-pmtr.html">pmTrsp</mi> $.
$s class pmSgn $: <mi href="df-psgn.html">pmSgn</mi> $.
$s class pmEven $: <mi href="df-evpm.html">pmEven</mi> $.

$( Matrix Algebra $)
$s class Mat $: <mi href="df-mat.html"> Mat </mi> $.
$s class DMat $: <mi href="df-dmat.html"> DMat </mi> $.
$s class ScMat $: <mi href="df-scmat.html"> ScMat </mi> $.
$s class DMatALT $: <mi href="df-dmatALT.html"> DMatALT </mi> $.
$s class ScMatALT $: <mi href="df-scmatALT.html"> ScMatALT </mi> $.
$s class maMul $: <mi href="df-mamu.html"> maMul </mi> $.
$s class maVecMul $: <mi href="df-mvmul.html"> maVecMul </mi> $.
$s class matRRep $: <mi href="df-marrep.html"> matRRep </mi> $.
$s class matRepV $: <mi href="df-marepv.html"> matRepV </mi> $.
$s class subMat $: <mi href="df-subma.html"> subMat </mi> $.
$s class subMat1 $: <msub href="df-smat.html"><mi> subMat </mi><mn> 1 </mn></msub> $.
$s class litMat $: <mi href="df-lmat.html"> litMat </mi> $.
$s class maDet $: <mi href="df-mdet.html"> maDet </mi> $.
$s class maAdju $: <mi href="df-madu.html"> maAdju </mi> $.
$s class minMatR1 $: <mi href="df-minmar1.html"> minMatR1 </mi> $.
$s class ConstPolyMat $: <mi href="df-cnstpmat.html">ConstPolyMat</mi> $.
$s class matToPolyMat $: <mi href="df-mat2pmat.html">matToPolyMat</mi> $.
$s class CharPlyMat $: <mi href="df-chpmat.html">CharPlyMat</mi> $.
$s class cPolyMatToMat $: <mi href="df-cpmat2mat.html"> cPolyMatToMat </mi> $.
$s class decompPMat $: <mi href="df-decpmat.html"> decompPMat </mi> $.
$s class pMatToMatPoly $: <mi href="df-pm2mp.html"> pMatToMatPoly </mi> $.

$s class MEndo $: <mi href="df-mend.html">MEndo</mi> $.
$s class SubDRing $: <mi href="df-sdrg.html">SubDRing</mi> $.
$s class Cntr $: <mi href="df-cntr.html">Cntr</mi> $.
$s class Cntz $: <mi href="df-cntz.html">Cntz</mi> $.
$s class CytP $: <mi href="df-cytp.html">CytP</mi> $.
$s class TopSep $: <mi href="df-topsep.html">TopSep</mi> $.
$s class TopLnd $: <mi href="df-toplnd.html">TopLnd</mi> $.

$( Steve Rodriguez $)
$s class lcm $: <mi href="df-lcm.html">lcm</mi> $. 
$s class _lcm $: <munder href="df-lcmf.html"><mi>lcm</mi> <mo>&#x5F;</mo></munder> $. 
$s class _Cc $: <msub href="df-bcc.html"><mo>C</mo> <mi>&#x1D450;</mi></msub> $. 


$( Andrew Salmon $)
$s class +r $: <msub href="df-addr.html"><mo>+</mo> <mi>r</mi></msub> $. 
$s class -r $: <msub href="df-subr.html"><mo>-</mo> <mi>r</mi></msub> $. 
$s class PtDf ( A , B ) $: <mrow> <mo>PtDf</mo> <mfenced>#A# #B#</mfenced></mrow> $.
$s class RR3 $: <mi href="df-rr3.html">RR3</mi> $.
$s class line3 $: <mi href="df-line3.html">line3</mi> $.


$( Glauco Siliprandi $)
$s class SAlg $: <mi href="df-salg.html">SAlg</mi> $.
$s class SalOn $: <mi href="df-salon.html">SalOn</mi> $.
$s class SalGen $: <mi href="df-salgen.html">SalGen</mi> $.
$s class sum^ $: <mi href="df-sumge0.html">sum^</mi> $.
$s class Meas $: <mi href="df-mea.html">Meas</mi> $.
$s class OutMeas $: <mi href="df-ome.html">OutMeas</mi> $.
$s class CaraGen $: <mi href="df-caragen.html">CaraGen</mi> $.
$s class voln* $: <mi href="df-ovoln.html">voln*</mi> $.
$s class voln $: <mi href="df-voln.html">voln</mi> $.
$s class SMblFn $: <mi href="df-smblfn.html">SMblFn</mi> $.
$s class liminf $: <mi href="df-liminf.html">lim inf</mi> $.
$s class ~~>* $: <munder accentunder href="df-xlim.html"><mo>&zigrarr;</mo><mi>*</mi></munder> $.


$( Alexander van der Vekens $)
$s class e// $: <mi href="df-nelbr">&notin;</mi> $.
$s class ~=c $: <msub href="df-cic.html"><mo>&#8771;</mo> <mi>&#x1D450;</mi></msub> $. 
$s wff F defAt A $: <mrow> #F# <mi href="df-dfat.html">defAt</mi> #A# </mrow> $.
$s class ( A ''' B ) $: <mfenced><mrow>#A# <mi href="df-afv.html">&#39&#39&#39</mi> #B#</mrow></mfenced> $.
$s class (( A F B )) $: <mfenced open="((" close="))"><mrow>#A# #F# #B#</mrow></mfenced> $.
$s class FriendGraph $: <mi href="df-frgr.html">FriendGraph</mi> $.
$s class Trails $: <mi href="df-trls.html">Trails</mi> $.
$s class TrailsOn $: <mi href="df-trlson.html">TrailsOn</mi> $.
$s class EdgWalks $: <mi href="df-ewlks.html">EdgWalks</mi> $.
$s class Walks $: <mi href="df-wlks.html">Walks</mi> $.
$s class WalksOn $: <mi href="df-wlkson.html">WalksOn</mi> $.

$s class linC $: <mi href="df-linc.html">linC</mi> $.
$s class LinCo $: <mi href="df-lco.html">LinCo</mi> $.
$s class linIndS $: <mi href="df-lininds.html">linIndS</mi> $.
$s class linDepS $: <mi href="df-lindeps.html">linDepS</mi> $.

$s class clLaw $: <mi href="df-cllaw.html">clLaw</mi> $.
$s class assLaw $: <mi href="df-asslaw.html">assLaw</mi> $.
$s class comLaw $: <mi href="df-comlaw.html">comLaw</mi> $.
$s class intOp $: <mi href="df-intop.html">intOp</mi> $.
$s class clIntOp $: <mi href="df-clintop.html">clIntOp</mi> $.
$s class assIntOp $: <mi href="df-assintop.html">assIntOp</mi> $.

$s class MgmALT $: <mi href="df-mgm2.html">MgmALT</mi> $.
$s class CMgmALT $: <mi href="df-cmgm2.html">CMgmALT</mi> $.
$s class SGrpALT $: <mi href="df-sgrp2.html">SGrpALT</mi> $.
$s class CSGrpALT $: <mi href="df-csgrp2.html">CSGrpALT</mi> $.

$s class prefix $: <mi href="df-pfx.html">prefix</mi> $.

$s class RePart $: <mi href="df-iccp.html">RePart</mi> $.
$s class FermatNo $: <mi href="df-fmtno.html">FermatNo</mi> $.
$s class Even $: <mi href="df-even.html">Even</mi> $.
$s class Odd $: <mi href="df-odd.html">Odd</mi> $.
$s class GoldbachEven $: <mi href="df-gbe.html">GoldbachEven</mi> $.
$s class GoldbachOddW $: <mi href="df-gbow.html">GoldbachOddW</mi> $.
$s class GoldbachOdd $: <mi href="df-gbo.html">GoldbachOdd</mi> $.

$s class UPWalks $: <mi href="df-upwlks.html">UPWalks</mi> $.
$s class Pairs $: <mi href="df-spr.html">Pairs</mi> $.

$s class /_f $: <msub href="df-fdiv"><mi>/</mi> <mi>f<mi></msub> $.
$s class _O $: <mi href="df-bigo">O</mi> $.
$s class #b $: <msub href="df-blen"><mi>#</mi> <mi>b<mi></msub> $.
$s class digit $: <mi href="df-dig.html">digit</mi> $.

$( David A. Wheeler $)
$s class >_ $: <mi href="df-gte.html"> &ge; </mi> $.
$s class > $: <mi href="df-gt.html"> &gt; </mi> $.
$s class sinh $: <mi href="df-sinh.html">sinh</mi> $.
$s class cosh $: <mi href="df-cosh.html">cosh</mi> $.
$s class tanh $: <mi href="df-tanh.html">tanh</mi> $.
$s class sec $: <mi href="df-sec.html">sec</mi> $.
$s class csc $: <mi href="df-csc.html">csc</mi> $.
$s class cot $: <mi href="df-cot.html">cot</mi> $.
$s class sgn $: <mi href="df-sgn.html">sgn</mi> $.
$s class logb $: <mi href="df-logb.html">logb</mi> $.
$s class log_ $: <mi href="df-log_.html">log_</mi> $.
$s wff A! x ( ph -> ps ) $: <mrow> <mo href="df-alsi.html">&forall;!</mo> #x# <mfenced mathcolor=#0D0 separators="">#ph# <mo mathcolor=#0D0>&rarr;</mo> #ps#</mfenced> </mrow> $.
$s wff A! x e. A ph $: <mrow> <mo href="df-alsc.html">&forall;!</mo> #x# <mo href="df-reu.html">&isin;</mo> #A# <mspace width=.4em /> #ph# </mrow> $.
$s wff A Reflexive B $: <mrow>#A# <mo href="df-reflexive.html">Reflexive</mo> #B#</mrow> $.
$s wff A Irreflexive B $: <mrow>#A# <mo href="df-irreflexive.html">Irreflexive</mo> #B#</mrow> $.


$( Emmett Weisz $)
$s class setrecs ( F ) $: <mrow> <mi href="df-setrecs">setrecs</mi> <mo>&ApplyFunction;</mo> <mfenced>#F#</mfenced> </mrow> $.
$s class Pg $: <mi href="df-pg.html">Pg</mi> $.


$( Richard Penner $)
$s wff A hereditary B $: <mrow>#A# <mo href="df-he.html">hereditary</mo> #B#</mrow> $.
$s class r* $: <mi href="df-rcl.html">r*</mi> $.

$( Alan Sare's Virtual Deduction $)
$s wff (. ph ->. ps ). $: <mfenced mathcolor=#0D0 separators="">#ph# <mo mathcolor=#0D0>&rarr;</mo> #ps#</mfenced> $.
$s wff (. ph ,. ps ->. ch ). $: <mfenced mathcolor=#0D0 separators="">#ph# <mo mathcolor=#0D0>,</mo> #ps# <mo mathcolor=#0D0>&rarr;</mo> #ch#</mfenced> $.
$s wff (. ph ,. ps ,. ch ->. th ). $: <mfenced mathcolor=#0D0 separators="">#ph# <mo mathcolor=#0D0>,</mo> #ps# <mo mathcolor=#0D0>,</mo> #ch# <mo mathcolor=#0D0>&rarr;</mo> #th#</mfenced> $.
$s wff (. ph ,. ps ). $: <mfenced mathcolor=#0D0>#ph# #ps#</mfenced> $.
$s wff (. ph ,. ps ,. ch ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ,. si ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze# #si#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ,. si ,. rh ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze# #si# #rh#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ,. si ,. rh ,. mu ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze# #si# #rh# #mu#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ,. si ,. rh ,. mu ,. la ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze# #si# #rh# #mu# #la#</mfenced> $.
$s wff (. ph ,. ps ,. ch ,. th ,. ta ,. et ,. ze ,. si ,. rh ,. mu ,. la ,. ka ). $: <mfenced mathcolor=#0D0>#ph# #ps# #ch# #th# #ta# #et# #ze# #si# #rh# #mu# #la# #ka#</mfenced> $.

$( Jonathan Ben-Naim's $)
$s class _pred ( X , A , R ) $: <mrow> <mo>pred</mo> <mfenced>#X# #A# #R#</mfenced></mrow> $.
$s wff A _Se B $: <mrow>#A# <mo href="df-bnj13.html">Se</mo> #B#</mrow> $.
$s wff A _FrSe B $: <mrow>#A# <mo href="df-bnj15.html">FrSe</mo> #B#</mrow> $.
$s class _trCl ( X , A , R ) $: <mrow> <mo>trCl</mo> <mfenced>#X# #A# #R#</mfenced></mrow> $.
$s wff _TrFo ( B , A , R ) $: <mrow> <mo>TrFo</mo> <mfenced>#B# #A# #R#</mfenced></mrow> $.


$( Benoit Jubin $)
$s class sngl A $: <mrow><mo href="df-bj-sngl.html">sngl</mo> #A#</mrow> $.
$s class tag A $: <mrow><mo href="df-bj-tag.html">tag</mo> #A#</mrow> $.
$s class (| A ,, B |) $: <mfenced open="&#x2985;" close="&#x2986;">#A# #B#</mfenced> $.
$s class pr1 A $: <mrow><mo href="df-bj-pr1.html">pr1</mo> #A#</mrow> $.
$s class pr2 A $: <mrow><mo href="df-bj-pr2.html">pr2</mo> #A#</mrow> $.
$s class Diag $: <mo href="df-bj-diag.html">Diag</mo> $.
$s class ( Diag ` A ) $: <msub><mo href="df-bj-diag.html">Diag</mo> #A#</msub> $.
$s class inftyexpi $: <mo href="df-bj-inftyexpi.html">inftyexpi</mo> $.
$s class pinfty $: <mo href="df-bj-pinfty.html">+&infin;</mo> $.
$s class minfty $: <mo href="df-bj-minfty.html">-&infin;</mo> $.
$s class RRbar $: <mover href="df-bj-rrbar.html"><mi>&Ropf;</mi> <mo>&oline;</mo></mover> $.
$s class RRhat $: <mover href="df-bj-rrhat.html"><mi>&Ropf;</mi> <mo>^</mo></mover> $.
$s class CCbar $: <mover href="df-bj-ccbar.html"><mi>&Copf;</mi> <mo>&oline;</mo></mover> $.
$s class CChat $: <mover href="df-bj-cchat.html"><mi>&Copf;</mi> <mo>^</mo></mover> $.
$s class CCinfty $: <msub href="df-bj-ccinfty"><mi>&Copf;</mi> <mi>&infin;</mi></msub> $.
$s class infty $: <mi href="df-bj-infty">&infin;</mi> $.
$s class prcpal $: <mi href="df-bj-prcpal">prcpal</mi> $.
$s class Arg $: <mi href="df-bj-arg">Arg</mi> $.
$s class +cc $: <msub href="df-bj-addc.html"><mo>+</mo> <mover><mi>&Copf;</mi> <mo>&oline;</mo></mover></msub> $.
$s class -cc $: <msub href="df-bj-oppc.html"><mo>-</mo> <mover><mi>&Copf;</mi> <mo>&oline;</mo></mover></msub> $.
$s class .cc $: <msub href="df-bj-mulc.html"><mo>&sdot;</mo> <mover><mi>&Copf;</mi> <mo>&oline;</mo></mover></msub> $.
$s class invc $: <msup href="df-bj-invc.html"><mo>&sdot;</mo> <mn>-1</mn></msup> $.
$s class RRVec $: <mi href="df-bj-rrvec.html">&Ropf;Vec</mi> $.

$s class Moore_ $: <munder href="df-bj-moore.html"><mi>Moore</mi> <mo>&#x5F;</mo></munder> $.
$s class -Set-> $: <munder accentunder href="df-bj-fset.html"><mo>&xrarr;</mo><mo>Set</mo></munder> $.
$s class -Top-> $: <munder accentunder href="df-bj-tophom.html"><mo>&xrarr;</mo><mo>Top</mo></munder> $.
$s class -Mgm-> $: <munder accentunder href="df-bj-magmahom.html"><mo>&xrarr;</mo><mo>Mgm</mo></munder> $.
$s class -TopMgm-> $: <munder accentunder href="df-bj-topmgmhom.html"><mo>&xrarr;</mo><mo>TopMgm</mo></munder> $.
$s wff F e. ( A -Set-> B ) $: <mrow> #F# <mo>:</mo> #A# <munder href="df-bj-fset.html"><mo>&xrarr;</mo><mo>Set</mo></munder> #B# </mrow> $.
$s wff F e. ( A -Top-> B ) $: <mrow> #F# <mo>:</mo> #A# <munder href="df-bj-tophom.html"><mo>&xrarr;</mo><mo>Top</mo></munder> #B# </mrow> $.
$s wff F e. ( A -Mgm-> B ) $: <mrow> #F# <mo>:</mo> #A# <munder href="df-bj-magmahom.html"><mo>&xrarr;</mo><mo>Mgm</mo></munder> #B# </mrow> $.
$s wff F e. ( A -TopMgm-> B ) $: <mrow> #F# <mo>:</mo> #A# <munder href="df-bj-topmgmhom.html"><mo>&xrarr;</mo><mo>TopMgm</mo></munder> #B# </mrow> $.
$s class curry_ $: <mi href="df-bj-cur">curry_</mi> $.
$s class uncurry_ $: <mi href="df-bj-unc">uncurry_</mi> $.

$s class [s B / A ]s S $: <mrow><mfenced open="[" close="]s" separators="/"> #B# #A# </mfenced> #S# </mrow> $.

$s wff Prv ph $: <mrow><mo href="ax-prv1.html">Prv</mo> #ph#</mrow> $.
$s wff F/ x e. A ph $:  <mrow> <mo href="df-bj-rnf.html">&#8498;</mo> #x# <mo>&isin;</mo> #A# <mspace width=.4em /> #ph# </mrow> $.
$s wff [b x /b y ]b ph $: <mrow><mfenced open="[b" close="]b" separators="/b"> #y# #x# </mfenced> #ph# </mrow> $.
$s wff if- ( ph , ps , ch ) $: <mrow> <mo href="df-bj-if.html">if-</mo> <mfenced>#ph# #ps# #ch#</mfenced></mrow> $.
$s class elwise $: <mi href="df-elwise.html">elwise</mi> $.
$s class ( A Proj B ) $: <mfenced><mrow>#A# <mo href="df-bj-proj.html">Proj</mo> #B#</mrow></mfenced> $.
$s class (| A |) $: <mfenced open="&#x2985;" close="&#x2986;">#A#</mfenced> $.
$s class FinSum $: <mo href="df-bj-finsum.html">FinSum</mo> $.

$( Peter Mazsa $)
$s class ( A |X. B ) $: <mrow> #A# <mo href="df-xrn.html">&ltimes;</mo> #B# </mrow> $.

$( Norm Megill $)
$s class <oL $: <msub href="df-lcv.html"><mo>&#8918;</mo> <mi>L</mi></msub> $.
$s class <o $: <mo href="df-covers.html">&#8918;</mo> $.
$s class ( <o ` A ) $: <msub><mo>&#8918;</mo> #A#</msub> $.
$s class LSAtoms $: <mi href="df-lsatoms.html">LSAtoms</mi> $.
$s class LSHyp $: <mi href="df-lshyp.html">LSHyp</mi> $.
$s class LFnl $: <mi href="df-lfl.html">LFnl</mi> $.
$s class LKer $: <mi href="df-lkr.html">LKer</mi> $.
$s class LDual $: <mi href="df-ldual.html">LDual</mi> $.
$s class OP $: <mi href="df-oposet.html">OP</mi> $.
$s class cm $: <mi href="df-cmtN.html">cm</mi> $.
$s class OL $: <mi href="df-ol.html">OL</mi> $.
$s class OML $: <mi href="df-oml.html">OML</mi> $.
$s class Atoms $: <mi href="df-ats.html">Atoms</mi> $.
$s class AtLat $: <mi href="df-atl.html">AtLat</mi> $.
$s class CvLat $: <mi href="df-cvlat.html">CvLat</mi> $.
$s class HL $: <mi href="df-hlat.html">HL</mi> $.
$s class LLines $: <mi href="df-llines.html">LLines</mi> $.
$s class LPlanes $: <mi href="df-lplanes.html">LPlanes</mi> $.
$s class LVols $: <mi href="df-lvols.html">LVols</mi> $.
$s class Lines $: <mi href="df-lines.html">Lines</mi> $.
$s class Points $: <mi href="df-pointsN.html">Points</mi> $.
$s class PSubSp $: <mi href="df-psubsp.html">PSubSp</mi> $.
$s class pmap $: <mi href="df-pmap.html">pmap</mi> $.
$s class PCl $: <mi href="df-pclN.html">PCl</mi> $.
$s class PSubCl $: <mi href="df-psubclN.html">PSubCl</mi> $.
$s class LHyp $: <mi href="df-lhyp.html">LHyp</mi> $.
$s class LAut $: <mi href="df-laut.html">LAut</mi> $.
$s class WAtoms $: <mi href="df-watsN.html">WAtoms</mi> $.
$s class PAut $: <mi href="df-pautN.html">PAut</mi> $.
$s class LDil $: <mi href="df-ldil.html">LDil</mi> $.
$s class LTrn $: <mi href="df-ltrn.html">LTrn</mi> $.
$s class Dil $: <mi href="df-dilN.html">Dil</mi> $.
$s class Trn $: <mi href="df-trnN.html">Trn</mi> $.
$s class trL $: <mi href="df-trl.html">trL</mi> $.
$s class TGrp $: <mi href="df-tgrp.html">TGrp</mi> $.
$s class TEndo $: <mi href="df-tendo.html">TEndo</mi> $.
$s class EDRing $: <mi href="df-edring.html">EDRing</mi> $.
$s class EDRingR $: <msub><mi>EDRing</mi> <mi>R</mi></msub> $.
$s class DVecA $: <mi href="df-dveca.html">DVecA</mi> $.
$s class DIsoA $: <mi href="df-disoa.html">DIsoA</mi> $.
$s class DVecH $: <mi href="df-dvech.html">DVecH</mi> $.
$s class ocA $: <mi href="df-docaN.html">ocA</mi> $.
$s class vA $: <mi href="df-djaN.html">vA</mi> $.
$s class DIsoB $: <mi href="df-dib.html">DIsoB</mi> $.
$s class DIsoC $: <mi href="df-dic.html">DIsoC</mi> $.
$s class DIsoH $: <mi href="df-dih.html">DIsoH</mi> $.
$s class ocH $: <mi href="df-doch.html">ocH</mi> $.
$s class joinH $: <mi href="df-djh.html">joinH</mi> $.
$s class LPol $: <mi href="df-lpolN.html">LPol</mi> $.
$s class LCDual $: <mi href="df-lcdual.html">LCDual</mi> $.
$s class mapd $: <mi href="df-mapd.html">mapd</mi> $.
$s class HVMap $: <mi href="df-hvmap.html">HVMap</mi> $.
$s class HDMap1 $: <mi href="df-hdmap1.html">HDMap1</mi> $.
$s class HDMap $: <mi href="df-hdmap.html">HDMap</mi> $.
$s class HGMap $: <mi href="df-hgmap.html">HGMap</mi> $.
$s class HLHil $: <mi href="df-hlhil.html">HLHil</mi> $.
$s class mapd $: <mi href="df-mapd.html">mapd</mi> $.

$( Jim Kingdon $)
$s class _tau $: <mi href="df-tau.html" mathvariant="normal"> &tau; </mi> $.

$( Schemes with unknown tokens:
$s class ==3 $: <mi> &#x2261;&#x2083; </mi> $.
$s class dst $: <mi href="df-dst.html">dst</mi> $.
$s class absv $: <mi href="df-absv.html">absv</mi> $.
$s class nrm $: <mi>nrm</mi> $.
$s class IndClsBu $: <mi href="df-indclsbu.html">IndClsBu</mi> $.
$s class ||g $: <mi>||g</mi> $.
$s class plane3 $: <mi>plane3</mi> $.
$s class trP $: <mi href="df-trp.html">trP</mi> $.
$s class _fns $: <mi> fns </mi> $.
$s class AtsLat $: <mi href="df-atslat.html">AtsLat</mi> $.
$s class ser $: <mi>ser</mi> $.
$s class fcard $: <mi href="df-fcard.html">fcard</mi> $.
$s class C_rng $: <mi>C_rng</mi> $.
$s class -vNEW $: <mi href="df-minusv.html">-vNEW</mi> $.
$s class RVecNEW $: <mi href="df-rvec.html">RVecNEW</mi> $.
$s class SubSpNEW $: <mi href="df-sbsp.html">SubSpNEW</mi> $.
$s class spanNEW $: <mi href="df-vspan.html">spanNEW</mi> $.
$s class o+ $: <mi href="df-oplus.html">o+</mi> $.
$s class /v $: <mi href="df-quov.html">/v</mi> $.
$s class normv $: <mi href="df-normv.html">normv</mi> $.
$s class sumP $: <mi href="df-sump.html">sumP</mi> $.
$s class BasesP $: <mi href="df-basesp.html">BasesP</mi> $.
$s class rankP $: <mi href="df-rankp.html">rankP</mi> $.
$s class PHyp $: <mi href="df-hyp.html">PHyp</mi> $.
$s class eImage $: <mi href="df-eimage.html">eImage</mi> $.
$s class *HRing $: <mi>*HRing</mi> $.
$)

$( Words $)
$s class Word A $: <mrow> <mi>Word</mi> #A# </mrow> $.
$s class <" A "> $: <mrow> <mo>&lang;&ldquo;</mo> #A# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C D "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C##D# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C D E "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C##D##E# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C D E F "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C##D##E##F# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C D E F G "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C##D##E##F##G# <mo>&rdquo;&rang;</mo> </mrow> $.
$s class <" A B C D E F G H "> $: <mrow> <mo>&lang;&ldquo;</mo> #A##B##C##D##E##F##G##H# <mo>&rdquo;&rang;</mo> </mrow> $.


$( Orders $)
$s wff R Po A $: <mrow> #R# <mi href="df-po.html">Po</mi> #A# </mrow> $.
$s wff R Or A $: <mrow> #R# <mi href="df-so.html">Or</mi> #A# </mrow> $.
$s wff R Fr A $: <mrow> #R# <mi href="df-fr.html">Fr</mi> #A# </mrow> $.
$s wff R Se A $: <mrow> #R# <mi href="df-se.html">Se</mi> #A# </mrow> $.
$s wff R We A $: <mrow> #R# <mi href="df-we.html">We</mi> #A# </mrow> $.
$s wff Ord A $: <mrow> <mi href="df-ord.html">Ord</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s wff Lim A $: <mrow> <mi href="df-lim.html">Lim</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class suc A $: <mrow> <mi href="df-suc.html">suc</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class AC_ A $: <mrow> <munder><mi href="df-acn.html">AC</mi> <mo>&#x5F;</mo></munder> #A# </mrow> $.


$(
@( Numerical constants @)
@s class 0 @: <mn> 0 </mn> @.
@s class 1 @: <mn> 1 </mn> @.
@s class 2 @: <mn> 2 </mn> @.
@s class 3 @: <mn> 3 </mn> @.
@s class 4 @: <mn> 4 </mn> @.
@s class 5 @: <mn> 5 </mn> @.
@s class 6 @: <mn> 6 </mn> @.
@s class 7 @: <mn> 7 </mn> @.
@s class 8 @: <mn> 8 </mn> @.
@s class 9 @: <mn> 9 </mn> @.
$)

$s class 10 $: <mn href="df-10.html"> 10 </mn> $.

$( Arithmetic number builder $)
$i class-n M $: <mi mathcolor=#808>M</mi> $.
$i class-n N $: <mi mathcolor=#808>N</mi> $.
$i class-n I $: <mi mathcolor=#808>I</mi> $.
$i class-n J $: <mi mathcolor=#808>J</mi> $.
$s class-n 0 $: 0 $.
$s class-n 1 $: 1 $.
$s class-n 2 $: 2 $.
$s class-n 3 $: 3 $.
$s class-n 4 $: 4 $.
$s class-n 5 $: 5 $.
$s class-n 6 $: 6 $.
$s class-n 7 $: 7 $.
$s class-n 8 $: 8 $.
$s class-n 9 $: 9 $.
$s class-n ; M N $: #M##N# $.
$s class -u N $: <mn>-#N#</mn> $.
$s class-n _ M N $: #M##N# $.
$s class . $: <mi href="df-dp.html">.</mi> $.
$s class-o ( M . N ) $: <mn>#M#<mi href="df-dp.html">.</mi>#N#</mn> $.
$s class-n ( M . N ) $: <mn>#M#<mi href="df-dp.html">.</mi>#N#</mn> $.
$s class ( M . N ) $: <mn>#M#<mi href="df-dp.html">.</mi>#N#</mn> $.

$( Special constants $)
$s class ( RR X. RR ) $: <msup> <mi> &Ropf; </mi> <mn>2</mn> </msup> $.
$s class-o ( RR X. RR ) $: <msup> <mi> &Ropf; </mi> <mn>2</mn> </msup> $.

$( Using token ` class-o ` as a type token for classes constructs without parenthesis, and ` O ` and ` P ` as identifiers for such cases. $)
$i class-o O $: <mi mathcolor=#808>O</mi> $.
$i class-o P $: <mi mathcolor=#808>P</mi> $.
$i class-o Q $: <mi mathcolor=#808>Q</mi> $.
$i class-o S $: <mi mathcolor=#808>S</mi> $.

$( Logics $)
$s wff -. ph $: <mrow> <mo href="wn.html">&not;</mo> #ph# </mrow> $.
$s wff ( ph -> ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.7em rspace=.7em href="wi.html">&rarr;</mo> #ps# </mrow></mfenced> $.
$s wff ( ph <-> ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.7em rspace=.7em href="df-bi.html">&harr;</mo> #ps# </mrow></mfenced> $.
$s wff ( ph /\ ps /\ ch ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3an.html">&and;</mo> #ps# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3an.html">&and;</mo> #ch# </mrow></mfenced> $.
$s wff ( ph \/ ps \/ ch ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3or.html">&or;</mo> #ps# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3or.html">&or;</mo> #ch# </mrow></mfenced> $.
$s wff ( ph /\ ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-an.html">&and;</mo> #ps# </mrow></mfenced> $.
$s wff ( ph \/ ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-or.html">&or;</mo> #ps# </mrow></mfenced> $.
$s wff ( ph -/\ ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-nan.html">&#8892;</mo> #ps# </mrow></mfenced> $.
$s wff ( ph \/_ ps ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-xor.html">&#8891</mo> #ps# </mrow></mfenced> $.

$( Quantifiers $)
$s wff A. x e. A ph $: <mrow> <mo href="df-ral.html">&forall;</mo> #x# <mo href="df-ral.html">&isin;</mo> #A# <mspace width=.4em /> #ph# </mrow> $.
$s wff E. x e. A ph $: <mrow> <mo href="df-rex.html">&exist;</mo> #x# <mo href="df-rex.html">&isin;</mo> #A# <mspace width=.4em /> #ph# </mrow> $.
$s wff E! x e. A ph $: <mrow> <mo href="df-reu.html">&exist;!</mo> #x# <mo href="df-reu.html">&isin;</mo> #A# <mspace width=.4em /> #ph# </mrow> $.
$s wff E* x e. A ph $: <mrow> <msup href="df-rmo.html"><mo>&exist;</mo><mo>*</mo></msup> #x# <mo href="df-rmo.html">&isin;</mo> #A# #ph# </mrow> $.
$s wff A. x ph $: <mrow> <mo href="wal.html">&forall;</mo> #x# <mspace width=.4em /> #ph# </mrow> $.
$s wff E. x ph $: <mrow> <mo href="df-ex.html">&exist;</mo> #x# <mspace width=.4em /> #ph# </mrow> $.
$s wff E! x ph $: <mrow> <mo href="df-eu.html">&exist;!</mo> #x# <mspace width=.4em /> #ph# </mrow> $.
$s wff E* x ph $: <mrow> <msup href="df-mo.html"><mo>&exist;</mo><mo>*</mo></msup> #x# <mspace width=.4em /> #ph# </mrow> $.
$s wff F/ x ph $: <mrow> <mo href="df-nf.html">&#8498;</mo> #x# <mspace width=.4em /> #ph# </mrow> $.
$s wff F/_ x A $: <mrow> <munder><mo href="df-nfc.html"> &#8498; </mo><mo> &#x5F; </mo></munder> #x# <mspace width=.4em /> #A# </mrow> $.
$s wff nfOLD x ph $: <mrow> <mo href="df-nfOLD.html">&#8498;OLD</mo> #x# <mspace width=.4em /> #ph# </mrow> $.




$( Classes and sets $)
$s wff O = P $: <mrow> #O# <mo href="wceq.html">=</mo> #P# </mrow> $.
$s wff O =/= P $: <mrow> #O# <mo href="df-ne.html">&ne;</mo> #P# </mrow> $.
$s wff O < P $: <mrow> #O# <mo href="df-ltxr.html"><</mo> #P# </mrow> $.
$s wff O <_ P $: <mrow> #O# <mo href="df-le.html">&le;</mo> #P# </mrow> $.
$s wff O <RR P $: <mrow> #O# <msub><mo href="df-lt.html">&lt;</mo> <mi>&Ropf;</mi></msub> #P# </mrow> $.
$s wff -. O C_ P $: <mrow> #O# <mo href="df-ss.html">&nsube;</mo> #P# </mrow> $.
$s wff O C_ P $: <mrow> #O# <mo href="df-ss.html">&sube;</mo> #P# </mrow> $.
$s wff O C. P $: <mrow> #O# <mo href="df-pss.html">&sub;</mo> #P# </mrow> $.
$s wff -. A e. B $: <mrow> #A# <mo href="df-nel.html">&notin;</mo> #B# </mrow> $.
$s wff A e/ B $: <mrow> #A# <mo href="df-nel.html">&notin;</mo> #B# </mrow> $.
$s wff [ y / x ] ph $: <mrow><mfenced open="[" close="]" separators="/"> #y# #x# </mfenced> #ph# </mrow> $.
$s wff [. A / x ]. ph $: <mrow><munder accentunder><mo fence>[</mo><mo>&#x02D9;</mo></munder>#A# <mo>/</mo> #x#<munder accentunder><mo fence>]</mo><mo>&#x02D9;</mo></munder> #ph#</mrow> $.
$s class [_ A / x ]_ B $: <mrow><mo fence>&#x298B;</mo> #A# <mo>/</mo> #x#<mo fence>&#x298C;</mo> #B#</mrow> $.
$s class { <. x , y >. | ph } $: <mfenced open="{" close="}"> <mrow><mfenced open="&lang;" close="&rang;">#x# #y#</mfenced> <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class { <. <. x , y >. , z >. | ph } $: <mfenced open="{" close="}"> <mrow><mfenced open="&lang;" close="&rang;"><mfenced open="&lang;" close="&rang;">#x# #y#</mfenced> #z#</mfenced> <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class { x e. A | ph } $: <mfenced open="{" close="}"> <mrow>#x# <mo href="df-rab.html">&isin;</mo> #A# <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class { x | ph } $: <mfenced open="{" close="}"><mrow> #x#  <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class ~P A $: <mrow> <mo from="prefix" href="df-pw.html">&#119979;</mo> #A# </mrow> $.
$s class ( A X. B ) $: <mfenced><mrow> #A# <mo href="df-xp.html">&times;</mo> #B# </mrow></mfenced> $.
$s class ( A u. B ) $: <mfenced><mrow> #A# <mo href="df-un.html">&cup;</mo> #B# </mrow></mfenced> $.
$s class ( A i^i B ) $: <mfenced><mrow> #A# <mo href="df-in.html">&cap;</mo> #B# </mrow></mfenced> $.
$s class ( A \ B ) $: <mfenced><mrow> #A# <mo href="df-dif.html">&ssetmn;</mo> #B# </mrow></mfenced> $.
$s class-o ( A X. B ) $: <mrow> #A# <mo href="df-xp.html">&times;</mo> #B# </mrow> $.
$s class-o ( A u. B ) $: <mrow> #A# <mo href="df-un.html">&cup;</mo> #B# </mrow> $.
$s class-o ( A i^i B ) $: <mrow> #A# <mo href="df-in.html">&cap;</mo> #B# </mrow> $.
$s class-o ( A \ B ) $: <mrow> #A# <mo href="df-dif.html">&ssetmn;</mo> #B# </mrow> $.
$s class { O , P , Q } $: <mfenced open="{" close="}"> #O# #P# #Q# </mfenced> $.
$s class { O , P } $: <mfenced open="{" close="}"> #O# #P# </mfenced> $.
$s class { O } $: <mfenced open="{" close="}"> #O# </mfenced> $.
$s class <. O , P , Q >. $: <mfenced open="&lang;" close="&rang;"> #O# #P# #Q# </mfenced> $.
$s class <. O , P >. $: <mfenced open="&lang;" close="&rang;"> #O# #P# </mfenced> $.
$s wff Smo A $: <mrow> <mi href="df-smo.html">Smo</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class [ A ] R $: <mrow><mfenced open="[" close="]"> #A# </mfenced> #R#</mrow> $.
$s class ( A /. R ) $: <mfenced><mrow> #A# <mo href="df-qs.html">/</mo> #R# </mrow></mfenced> $.
$s class-o ( A /. R ) $: <mrow> #A# <mo href="df-qs.html">/</mo> #R# </mrow> $.
$s wff R Er A $: <mrow>#R# <mi href="df-er.html">Er</mi> #A#</mrow> $.
$s wff Tr A $: <mrow> <mi href="df-tr.html">Tr</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s wff Rel R $: <mrow> <mi href="df-rel.html">Rel</mi> <mo>&ApplyFunction;</mo> #R# </mrow> $.
$s wff Fun A $: <mrow> <mi href="df-fun.html">Fun</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class dom A $: <mrow> <mi href="df-dm.html">dom</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class ran A $: <mrow> <mi href="df-rn.html">ran</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class oF R $: <mrow> <msub href="df-of.html"><mo>&compfn;</mo> <mi>f</mi></msub> <mo>&ApplyFunction;</mo> #R# </mrow> $. $( was &fnof; $)
$s class oR R $: <mrow> <msub href="df-ofr.html"><mo>&compfn;</mo> <mi>r</mi></msub> <mo>&ApplyFunction;</mo> #R# </mrow> $.
$s class oFC R $: <mrow> <msub href="df-ofc.html"><mo>&compfn;</mo> <mi>fc</mi></msub> <mo>&ApplyFunction;</mo> #R# </mrow> $. $( was &fnof; $)
$s class ( F oF R G ) $: <mfenced><mrow>#F# <msub>#R# <mi href="df-of.html">f</mi></msub> #G#</mrow></mfenced> $.
$s class-o ( F oF R G ) $: <mrow>#F# <msub>#R# <mi href="df-of.html">f</mi></msub> #G#</mrow> $.
$s wff F oR R G $: <mrow>#F# <msub>#R# <mi href="df-ofr.html">f</mi></msub> #G#</mrow> $.
$s class ( F supp Z ) $: <mrow><msub><mo href="df-supp.html">supp</mo> #Z#</msub><mo>&ApplyFunction;</mo> <mfenced>#F#</mfenced> </mrow> $.
$s wff F finSupp Z $: <mrow><msub><mo href="df-fsupp.html">finSupp</mo> #Z#</msub><mo>&ApplyFunction;</mo> <mfenced>#F#</mfenced> </mrow> $.

$( Functions $)
$s class `' A $: <msup> #A# <mn href="df-cnv.html">-1</mn> </msup> $.
$s class ( A " O ) $: <mrow> #A# <mfenced open="[" close="]">#O#</mfenced> </mrow> $. $( Removed stretchy="false" $)
$s class ( A o. B ) $: <mfenced><mrow> #A# <mo href="df-co.html">&compfn;</mo> #B# </mrow></mfenced> $.
$s class ( A |` B ) $: <mfenced><msub><mrow> #A# <mo href="df-res.html">&uharr;</mo></mrow> #B# </msub></mfenced> $.
$s class ( A ^m B ) $: <mfenced><msup> #A# #B# </msup></mfenced> $.
$s class-o ( A o. B ) $: <mrow> #A# <mo href="df-co.html">&compfn;</mo> #B# </mrow> $.
$s class-o ( A |` B ) $: <msub><mrow> #A# <mo href="df-res.html">&uharr;</mo></mrow> #B# </msub> $.
$s class-o ( A ^m B ) $: <msup> #A# #B# </msup> $.
$s wff A Fn B $:  <mrow> #A# <mo href="df-fn.html">Fn</mo> #B# </mrow> $.


$( Arithmetics $)
$s class ( O / P ) $: <mfenced><mfrac> #O# #P# </mfrac></mfenced> $.
$s class-o ( O / P ) $: <mfrac> #O# #P# </mfrac> $.
$s class -u ( O / P ) $: <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> <mfrac> #O# #P# </mfrac> </mrow></mfenced> $.
$s class-o -u ( O / P ) $: <mrow><mo form="prefix" href="df-nrg.html">&minus;</mo> <mfrac> #O# #P# </mfrac> </mrow> $.
$s class -u A $: <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow></mfenced> $.
$s class-o -u A $: <mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow> $.
$s class -e A $: <mfenced><mrow><mo form="prefix" href="df-xneg.html">&minus;</mo> #A# </mrow></mfenced> $.
$s class-o -e A $: <mrow><mo form="prefix" href="df-xneg.html">&minus;</mo> #A# </mrow> $.
$s class ( sqrt ` O ) $: <msqrt> #O# </msqrt> $.
$s class ( * ` O ) $: <mover> #O# <mo>&oline;</mo></mover> $.
$s class ( sin ` A ) $: <mrow> <mi href="df-sin.html">sin</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class ( cos ` A ) $: <mrow> <mi href="df-cos.html">cos</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class ( tan ` A ) $: <mrow> <mi href="df-tan.html">tan</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class ( log ` A ) $: <mrow> <mi href="df-log.html">log</mi> <mo>&ApplyFunction;</mo> #A# </mrow> $.
$s class ( abs ` O ) $: <mfenced open="|" close="|">#O#</mfenced> $.
$s class ( exp ` O ) $: <msup><mi href="df-ef.html" mathvariant="normal">e</mi> #O#</msup> $.
$s class ( logb ` O ) $: <msub><mi href="df-logb.html">log</mi> #O#</msub> $.
$s class-o ( O logb A ) $: <mrow><msub><mi href="df-logb.html">log</mi> #O#</msub> #A#</mrow> $.
$s class ( O logb A ) $: <mrow><msub><mi href="df-logb.html">log</mi> #O#</msub> #A#</mrow> $.
$s class ( # ` O ) $: <mfenced open="|" close="|">#O#</mfenced> $.
$s class ( |_ ` O ) $: <mfenced open="&lfloor;" close="&rfloor;">#O#</mfenced> $.
$s class ( |^ ` O ) $: <mfenced open="&lceil;" close="&rceil;">#O#</mfenced> $.
$s class ( ! ` A ) $: <mrow>#A# <mo form="postfix" href="df-fac.html">&excl;</mo></mrow> $.

$( Minus sign and exponents : make sure brackets are added. $)
$s class ( -u A ^ O ) $: <msup> <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow></mfenced> #O# </msup> $.
$s class ( -u A ^c O ) $: <msup> <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow></mfenced> #O# </msup> $.
$s class-o ( -u A ^ O ) $: <msup> <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow></mfenced> #O# </msup> $.
$s class-o ( -u A ^c O ) $: <msup> <mfenced><mrow><mo form="prefix" href="df-neg.html">&minus;</mo> #A# </mrow></mfenced> #O# </msup> $.


$( Composing exponents $)
$s class ( ( A ^ O ) ^ P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class ( ( A ^ O ) ^c P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class ( ( A ^c O ) ^ P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class ( ( A ^c O ) ^c P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class-o ( ( A ^ O ) ^ P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class-o ( ( A ^ O ) ^c P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class-o ( ( A ^c O ) ^ P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.
$s class-o ( ( A ^c O ) ^c P ) $: <msup> <mfenced><msup> #A# #O# </msup></mfenced> #P# </msup> $.

$s class ( A ^ O ) $: <msup> #A# #O# </msup> $.
$s class ( A ^c O ) $: <msup> #A# #O# </msup> $.
$s class-o ( A ^ O ) $: <msup> #A# #O# </msup> $.
$s class-o ( A ^c O ) $: <msup> #A# #O# </msup> $.

$( Intervals $)
$s class ( O [,] P ) $: <mfenced open='[' close=']'> #O# #P# </mfenced> $.
$s class ( O [,) P ) $: <mfenced open='[' close=')'> #O# #P# </mfenced> $.
$s class ( O (,] P ) $: <mfenced open='(' close=']'> #O# #P# </mfenced> $.
$s class ( O (,) P ) $: <mfenced open='(' close=')'> #O# #P# </mfenced> $.
$s class ( O ... P ) $: <mfenced><mrow>#O# <mo href="df-fz.html">&hellip;</mo> #P#</mrow></mfenced> $.
$s class ( O ..^ P ) $: <mfenced><mrow>#O# <mo href="df-fzo.html">..^</mo> #P#</mrow></mfenced> $.
$s class-o ( O [,] P ) $: <mfenced open='[' close=']'> #O# #P# </mfenced> $.
$s class-o ( O [,) P ) $: <mfenced open='[' close=')'> #O# #P# </mfenced> $.
$s class-o ( O (,] P ) $: <mfenced open='(' close=']'> #O# #P# </mfenced> $.
$s class-o ( O (,) P ) $: <mfenced open='(' close=')'> #O# #P# </mfenced> $.
$s class-o ( O ... P ) $: <mfenced><mrow>#O# <mo href="df-fz.html">&hellip;</mo> #P#</mrow></mfenced> $.
$s class-o ( O ..^ P ) $: <mfenced><mrow>#O# <mo href="df-fzo.html">..^</mo> #P#</mrow></mfenced> $.


$( Associativity for addition $)
$s class ( ( A + B ) + ( C + D ) ) $: <mfenced><mrow>#A# <mo href="df-add.html">+</mo> #B# <mo href="df-add.html">+</mo> #C# <mo href="df-add.html">+</mo> #D# </mrow></mfenced> $.
$s class ( ( A + B ) + C ) $: <mfenced><mrow>#A# <mo href="df-add.html">+</mo> #B# <mo href="df-add.html">+</mo> #C# </mrow></mfenced> $.
$s class ( A + ( B + C ) ) $: <mfenced><mrow>#A# <mo href="df-add.html">+</mo> #B# <mo href="df-add.html">+</mo> #C# </mrow></mfenced> $.

$s class ( A + ( B - C ) ) $: <mfenced><mrow>#A# <mo href="df-add.html">+</mo> #B# <mo href="df-sub.html">-</mo> #C# </mrow></mfenced> $.
$s class ( ( A - B ) + C ) $: <mfenced><mrow>#A# <mo href="df-sub.html">-</mo> #B# <mo href="df-add.html">+</mo> #C# </mrow></mfenced> $.
$s class ( ( A + B ) - C ) $: <mfenced><mrow>#A# <mo href="df-add.html">+</mo> #B# <mo href="df-sub.html">-</mo> #C# </mrow></mfenced> $.
$s class ( ( A - B ) - C ) $: <mfenced><mrow>#A# <mo href="df-sub.html">-</mo> #B# <mo href="df-sub.html">-</mo> #C# </mrow></mfenced> $.

$s class ( -u A + B ) $: <mfenced><mrow> <mo>-</mo> #A# <mo href="df-add.html">+</mo> #B# </mrow></mfenced> $.
$s class ( -u A - B ) $: <mfenced><mrow> <mo>-</mo> #A# <mo href="df-sub.html">-</mo> #B# </mrow></mfenced> $.

$( Associativity for addition non-fenced expressions $)
$s class-o ( ( A + B ) + ( C + D ) ) $: <mrow>#A# <mo>+</mo> #B# <mo>+</mo> #C# <mo>+</mo> #D# </mrow> $.
$s class-o ( ( A + B ) + C ) $: <mrow>#A# <mo>+</mo> #B# <mo>+</mo> #C# </mrow> $.
$s class-o ( A + ( B + C ) ) $: <mrow>#A# <mo>+</mo> #B# <mo>+</mo> #C# </mrow> $.

$s class-o ( A + ( B - C ) ) $: <mrow>#A# <mo>+</mo> #B# <mo>-</mo> #C# </mrow> $.
$s class-o ( ( A - B ) + C ) $: <mrow>#A# <mo>-</mo> #B# <mo>+</mo> #C# </mrow> $.
$s class-o ( ( A + B ) - C ) $: <mrow>#A# <mo>+</mo> #B# <mo>-</mo> #C# </mrow> $.
$s class-o ( ( A - B ) - C ) $: <mrow>#A# <mo>-</mo> #B# <mo>-</mo> #C# </mrow> $.

$s class-o ( -u A + B ) $: <mrow> <mo href="df-neg.html">-</mo> #A# <mo>+</mo> #B# </mrow> $.
$s class-o ( -u A - B ) $: <mrow> <mo href="df-neg.html">-</mo> #A# <mo>-</mo> #B# </mrow> $.

$( No need for additional rules for associativity for multiplication, as it is already not fenced $)
$( No need for additional rules for precedence of multiplication over addition as it is already not fenced. $)
$( Precedence of multiplication over addition - no need for additional rules, multiplication is already not fenced. $)

$( Multiplication : invisible times or dot $)
$s class ( M x. N ) $: <mrow> <mn>#M#</mn> <mo href="df-mul.html">&sdot;</mo> <mn>#N#</mn> </mrow> $.
$s class ( 0 x. A ) $: <mrow> <mn href="df-0.html">0</mn> <mo href="df-mul.html">&sdot;</mo> #A# </mrow> $. $( Add a dot when multiplying with zero, as this is not commonly written. $)
$s class ( A x. M ) $: <mrow> #A# <mo href="df-mul.html">&sdot;</mo> <mn>#M#</mn> </mrow> $. $( Add a dot when right-multiplying with a number, as this is not commonly written. $)
$s class ( A x. B ) $: <mrow> #A# <mo>&InvisibleTimes;</mo> #B# </mrow> $.
$s class-o ( M x. N ) $: <mrow> <mn>#M#</mn> <mo href="df-mul.html">&sdot;</mo> <mn>#N#</mn> </mrow> $.
$s class-o ( 0 x. A ) $: <mrow> <mn href="df-0.html">0</mn> <mo href="df-mul.html">&sdot;</mo> #A# </mrow> $. $( Add a dot when multiplying with zero, as this is not commonly written. $)
$s class-o ( A x. M ) $: <mrow> #A# <mo href="df-mul.html">&sdot;</mo> <mn>#M#</mn> </mrow> $. $( Add a dot when right-multiplying with a number, as this is not commonly written. $)
$s class-o ( A x. B ) $: <mrow> #A# <mo>&InvisibleTimes;</mo> #B# </mrow> $.

$( Algebraic Constructs $)
$s class ( Base ` A ) $: <msub><mi href="df-base.html">Base</mi> #A#</msub> $.
$s class ( 0g ` A ) $: <msub><mn href="df-0g.html">0</mn> #A#</msub> $.
$s class ( .g ` A ) $: <msub><mo href="df-mulg.html">&sdot;</mo> #A#</msub> $.
$s class ( +g ` A ) $: <msub><mo href="df-plusg.html">+</mo> #A#</msub> $.
$s class ( -g ` A ) $: <msub><mo href="df-sbg.html">-</mo> #A#</msub> $.
$s class ( 1r ` A ) $: <msub><mn href="df-ur.html">1</mn> #A#</msub> $.
$s class ( *r ` A ) $: <msub><mn href="df-starv.html">*</mn> #A#</msub> $.
$s class ( .r ` A ) $: <msub><mo href="df-mulr.html">&sdot;</mo> #A#</msub> $.
$s class ( .s ` A ) $: <msub><mo href="df-vsca.html">&sdot;</mo> #A#</msub> $.
$s class ( le ` A ) $: <msub><mo href="df-ple.html">&le;</mo> #A#</msub> $.
$s class ( lt ` A ) $: <msub><mo href="df-plt.html">&lt;</mo> #A#</msub> $.
$s class ( mulGrp ` A ) $: <msub><mi href="df-mgp.html">mulGrp</mi> #A#</msub> $.
$s class ( ( *r ` A ) ` B ) $: <msup>#B# <msub><mn href="df-starv.html">*</mn> #A#</msub></msup> $.
$s class ( Z/nZ ` A ) $: <mrow><mi href="df-zn.html">&Zopf;</mi><mo>/</mo>#A#<mi href="df-zn.html">&Zopf;</mi></mrow> $.

$( Constructs $)
$s class ( O _C P ) $: <mrow> <mo>(</mo> <mfrac linethickness="0">#O# #P#</mfrac><mo>)</mo> </mrow> $.
$s class-o ( O _C P ) $: <mrow> <mo>(</mo> <mfrac linethickness="0">#O# #P#</mfrac><mo>)</mo> </mrow> $.
$s class ( x e. A , y e. B , z e. C |-> O ) $: <mfenced> <mrow> #x# <mo href="df-bj-mpt3.html">&isin;</mo> #A# <mo>,</mo> #y# <mo href="df-bj-mpt3.html">&isin;</mo> #B# <mo>,</mo> #z# <mo href="df-bj-mpt3.html">&isin;</mo> #C# <mo href="df-bj-mpt3.html">&longmapsto;</mo> #O# </mrow></mfenced> $.
$s class ( x e. A , y e. B |-> O ) $: <mfenced> <mrow> #x# <mo href="df-mpt2.html">&isin;</mo> #A# <mo>,</mo> #y# <mo href="df-mpt2.html">&isin;</mo> #B# <mo href="df-mpt2.html">&longmapsto;</mo> #O# </mrow></mfenced> $.
$s class ( x e. A |-> O ) $: <mfenced> <mrow> #x# <mo href="df-mpt.html">&isin;</mo> #A# <mo href="df-mpt.html">&longmapsto;</mo> #O# </mrow></mfenced> $.
$s class if ( ph , O , P ) $: <mrow> <mo href="df-if.html">if</mo> <mfenced>#ph# #O# #P#</mfenced></mrow> $.
$s class sup ( O , P , Q ) $: <mrow> <mo href="df-sup.html">sup</mo> <mfenced>#O# #P# #Q#</mfenced></mrow> $.
$s class inf ( O , P , Q ) $: <mrow> <mo href="df-inf.html">sup</mo> <mfenced>#O# #P# #Q#</mfenced></mrow> $.
$s class |^|_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-uni.html">&xcap;</mo> <mrow>#x# <mo>=</mo> #O#</mrow> #P# </munderover> #A# </mrow> $.
$s class U_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-iun.html">&xcup;</mo> <mrow>#x# <mo>=</mo> #O#</mrow> #P# </munderover> #A# </mrow> $.
$s wff Disj_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-disj.html">Disj</mo> <mrow>#x# <mo>=</mo> #O#</mrow> #P# </munderover> #A# </mrow> $.
$s class sum_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-sum.html">&sum;</mo><mrow> #x# <mo>=</mo> #O# </mrow> #P# </munderover> #A# </mrow> $.
$s class sum* x e. ( O ... P ) A $: <mrow><munderover><msup><mo href="df-esum.html">&sum;</mo> <mi>*</mi></msup><mrow> #x# <mo>=</mo> #O# </mrow> #P# </munderover> #A# </mrow> $.
$s class prod_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-prod.html">&prod;</mo><mrow> #x# <mo>=</mo> #O# </mrow> #P# </munderover> #A# </mrow> $.
$s class X_ x e. ( O ... P ) A $: <mrow><munderover><mo href="df-ixp.html">&#x2a09;</mo><mrow> #x# <mo>=</mo> #O# </mrow> #P# </munderover> #A# </mrow> $.
$s class |^|_ x e. O A $: <mrow><munder><mo href="df-iin.html">&xcap;</mo> <mrow>#x# <mo>&isin;</mo> #O#</mrow></munder> #A# </mrow> $.
$s class U_ x e. O A $: <mrow><munder><mo href="df-iun.html">&xcup;</mo> <mrow>#x# <mo>&isin;</mo> #O#</mrow></munder> #A# </mrow> $.
$s wff Disj_ x e. O A $: <mrow><munder><mo href="df-disj.html">Disj</mo> <mrow>#x# <mo>&isin;</mo> #O#</mrow></munder> #A# </mrow> $.
$s class sum_ x e. O A $: <mrow><munder><mo href="df-sum.html">&sum;</mo><mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #A# </mrow> $.
$s class sum* x e. O A $: <mrow><munder><msup><mo href="df-esum.html">&sum;</mo> <mi>*</mi></msup><mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #A# </mrow> $.
$s class prod_ x e. O A $: <mrow><munder><mo href="df-prod.html">&prod;</mo><mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #A# </mrow> $.
$s class X_ x e. O A $: <mrow><munder><mo href="df-ixp.html">&#x2a09;</mo><mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #A# </mrow> $.
$s class ( Q gsum ( x e. ( O ... P ) |-> B ) ) $: <mfenced><munderover><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> <mrow> #x# <mo>=</mo> #O# </mrow> #P#</munderover> #B#</mfenced> $.
$s class ( Q gsum ( x e. O |-> B ) ) $: <mfenced><munder><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> <mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #B#</mfenced> $.
$s class ( Q gsum A ) $: <mfenced><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> #A#</mfenced> $.
$s class-o ( Q gsum ( x e. ( O ... P ) |-> B ) ) $: <mrow><munderover><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> <mrow> #x# <mo>=</mo> #O# </mrow> #P#</munderover> #B#</mrow> $.
$s class-o ( Q gsum ( x e. O |-> B ) ) $: <mrow><munder><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> <mrow> #x# <mo>&isin;</mo> #O# </mrow></munder> #B#</mrow> $.
$s class-o ( Q gsum A ) $: <mrow><msub><mo href="df-gsum.html">&Sum;</mo> #Q#</msub> #A#</mrow> $.
$s class |^| A $: <mrow> <mo href="df-int.html">&xcap;</mo> #A# </mrow> $.
$s class U. A $: <mrow> <mo href="df-uni.html">&xcup;</mo> #A# </mrow> $.
$s class recs ( F ) $: <mrow> <mi href="df-recs.html">recs</mi> <mo>&ApplyFunction;</mo> <mfenced>#F#</mfenced> </mrow> $. $( Removed stretchy="false" $)
$s class rec ( F , O ) $: <mrow> <mi href="df-rdg.html">rec</mi> <mo>&ApplyFunction;</mo> <mfenced> #F# #O# </mfenced> </mrow> $. $( Removed stretchy="false" $)
$s class wrecs ( R , O , P ) $: <mrow> <mi href="df-wrecs.html">wrecs</mi> <mo>&ApplyFunction;</mo> <mfenced> #R# #O# #P# </mfenced> </mrow> $. $( Removed stretchy="false" $)
$s class seq A ( .+ , F ) $: <mrow> <mo href="df-seq.html">seq</mo> #A# <mfenced> #.+# #F# </mfenced></mrow> $.
$s class ( iota x ph ) $: <mfenced> <mrow><mo href="df-iota.html">&iota;</mo> #x# <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class ( iota_ x e. A ph ) $: <mfenced> <mrow><mo href="df-iota.html">&iota;</mo> #x# <mo>&isin;</mo> #A# <mo lspace=.3em rspace=.3em>|</mo> #ph# </mrow></mfenced> $.
$s class ( ZZ>= ` A ) $: <msub> <mi href="df-uz.html">&Zopf;</mi> <mrow> <mo href="df-uz.html">&ge;</mo> #A# </mrow> </msub> $.
$s class S. A B _d x $:  <mrow> <msub> <mo href="df-itg.html"> &#x222B;</mo> #A# </msub> #B# <mo>d</mo>#x#</mrow> $.
$s class S_ [ A -> B ] C _d x $: <mrow> <msubsup> <mo href="df-ditg.html"> &#x222B;</mo> #A# #B# </msubsup> #C# <mo>d</mo>#x#</mrow> $.
$s class-o ( A _D ( x e. B |-> O ) ) $: <mfrac><mrow><mo href="df-dv.html">d</mo><mfenced separators="&longmapsto;"><mrow>#x# <mo>&isin;</mo> #B#</mrow> #O#</mfenced></mrow> <mrow><msub><mo href="df-dv.html">d</mo>#A#</msub> #x#</mrow></mfrac> $.
$s class ( A _D ( x e. B |-> O ) ) $: <mfrac><mrow><mo href="df-dv.html">d</mo><mfenced separators="&longmapsto;"><mrow>#x# <mo>&isin;</mo> #B#</mrow> #O#</mfenced></mrow> <mrow><msub><mo href="df-dv.html">d</mo>#A#</msub> #x#</mrow></mfrac> $.
$s class ( A _D F ) $: <msubsup>#F# #A# <mo href="df-dv.html">&#x2032;</mo></msubsup> $.
$( s class ( A _D F ) $: <mfenced><msubsup>#F# #A# <mo href="df-dv.html">&#x2032;</mo></msubsup></mfenced> $)
$s wff F : O --> P $: <mrow> #F# <mo>:</mo> #O# <mo href="df-f.html">&xrarr;</mo> #P# </mrow> $.
$s wff F : O -1-1-> P $: <mrow> #F# <mo>:</mo> #O# <munder href="df-f1.html"><mo>&xrarr;</mo> <mo>1-1</mo></munder> #P# </mrow> $.
$s wff F : O -onto-> P $: <mrow> #F# <mo>:</mo> #O# <munder href="df-fo.html"><mo>&xrarr;</mo> <mo>onto</mo></munder> #P# </mrow> $.
$s wff F : O -1-1-onto-> P $: <mrow> #F# <mo>:</mo> #O# <munder href="df-f1o.html"><mo>&xrarr;</mo> <mo>1-1 onto</mo></munder> #P# </mrow> $.
$s wff F e. ( A -cn-> B ) $: <mrow> #F# <mo>:</mo> #A# <munder href="df-cncf.html"><mo>&xrarr;</mo><mo>cn</mo></munder> #B# </mrow> $.
$s wff hadd ( ph , ps , ch ) $: <mrow> <mo href="df-had.html">hadd</mo> <mfenced>#ph# #ps# #ch#</mfenced></mrow> $.
$s wff cadd ( ph , ps , ch ) $: <mrow> <mo href="df-cad.html">cadd</mo> <mfenced>#ph# #ps# #ch#</mfenced></mrow> $.
$s wff CondEq ( x = y -> ph ) $: <mrow> <mo href="df-cdeq.html">CondEq</mo> <mfenced><mrow>#x# <mo>=</mo> #y# <mo>&rarr;</mo> #ph#</mrow></mfenced></mrow> $.
$s wff H Isom O , P ( Q , S ) $: <mrow> #H# <msub><mo href="df-isom.html">Isom</mo> <mrow>#O# <mo>,</mo> #P#</mrow></msub> <mfenced>#Q# #S#</mfenced></mrow> $.
$s class OrdIso ( O , P ) $: <mrow> <mo href="df-oi.html">OrdIso</mo> <mfenced>#O# #P#</mfenced></mrow> $.
$s class seqom ( O , P ) $: <mrow> <msub href="df-seqom.html"><mo>seq</mo> <mi>&omega;</mi></msub> <mfenced>#O# #P#</mfenced></mrow> $.

$s class Locally A $: <mrow><mo href="df-lly.html">Locally<mo> #A# </mrow> $.
$s class N-Locally A $: <mrow><mo href="df-nlly.html">N-Locally<mo> #A# </mrow> $.
$s wff Prt A $: <mrow><mo href="df-prt.html">Prt<mo> #A# </mrow> $.

$( These definitions are placed later because they are overridden by some constructs $)
$s wff O e. A $: <mrow> #O# <mo href="wcel.html">&isin;</mo> #A# </mrow> $.
$s class ( F ` O ) $: <mrow> #F# <mo>&ApplyFunction;</mo> <mfenced>#O#</mfenced> </mrow> $. $( Removed <mo fence stretchy="false">(</mo> $)

$( From Mathboxes $)
$s wff ( ph -/\ ps -/\ ch ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3nand.html">&#8892;</mo> #ps# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-3nand.html">&#8892;</mo> #ch# </mrow></mfenced> $.
$s wff ( ph /\ ps /\ ch /\ th ) $: <mfenced><mrow> #ph# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-bnj17.html">&and;</mo> #ps# <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-bnj17.html">&and;</mo> #ch#  <mo linebreak=goodbreak lspace=.5em rspace=.5em href="df-bnj17.html">&and;</mo> #th# </mrow></mfenced> $.


$( Relation Constants $)
$s class ~~ $: <mo href="df-en.html">&ap;</mo> $.
$s class ~< $: <mo href="df-sdom.html">&pr;</mo> $.
$s class ~<_ $: <mo href="df-dom.html">&prcue;</mo> $.
$s class ~<_* $: <msup href="df-wdom.html"><mo>&prcue;</mo> <mo>*</mo></msup> $.
$s class ~~> $: <mo href="df-clim.html">&zigrarr;</mo> $. $( I preferred &dzigrarr; , but that one is not the MathJax fonts. $)
$s class ~~>r $: <munder accentunder href="df-rlim.html"><mo>&zigrarr;</mo><mi>&Ropf;</mi></munder> $.
$s class ~~>t $: <munder accentunder href="df-lm.html"><mo>&zigrarr;</mo><mi>t</mi></munder> $.
$s class ~~>u $: <munder accentunder href="df-ulm.html"><mo>&zigrarr;</mo><mi>u</mi></munder> $.
$s class ~~>v $: <munder accentunder href="df-hlim.html"><mo>&zigrarr;</mo><mi>v</mi></munder> $.
$s class <_ $: <mo href="df-le.html">&le;</mo> $.
$s class < $: <mo href="df-ltxr.html">&lt;</mo> $.
$s class <RR $: <msub href="df-lt.html"><mo>&lt;</mo> <mi>&Ropf;</mi></msub> $.
$s class [C.] $: <mo href="df-rpss.html">[&sub;]</mo> $.

$( Function-like constructs $)
$s class tpos F $: <mrow><mo href="df-tpos.html">tpos</mo> #F#</mrow> $.
$s class curry F $: <mrow><mo href="df-cur.html">curry</mo> #F#</mrow> $.
$s class uncurry F $: <mrow><mo href="df-unc.html">uncurry</mo> #F#</mrow> $.

$( Function Constants $)
$s class || $: <mo href="df-dvds.html">&par;</mo> $.
$s class # $: <mfenced open="|" close="|" href="df-hash.html"><mi>.</mi></mfenced> $.
$s class ! $: <mo href="df-fac.html">&excl;</mo> $.
$s class har $: <mo href="df-har.html">har</mo> $.
$s class fi $: <mo href="df-fi.html">fi</mo> $.
$s class shift $: <mo href="df-shft.html">shift</mo> $.
$s class abs $: <mo href="df-abs.html">abs</mo> $.
$s class log $: <mo href="df-log.html">log</mo> $.
$s class exp $: <mo href="df-ef.html">exp</mo> $.
$s class sin $: <mo href="df-sin.html">sin</mo> $.
$s class cos $: <mo href="df-cos.html">cos</mo> $.
$s class tan $: <mo href="df-tan.html">tan</mo> $.
$s class arcsin $: <mo href="df-asin.html">arcsin</mo> $.
$s class arccos $: <mo href="df-acos.html">arccos</mo> $.
$s class arctan $: <mo href="df-atan.html">arctan</mo> $.
$s class 1st $: <msup href="df-1st.html"><mo>1</mo> <mo>st</mo></msup> $.
$s class 2nd $: <msup href="df-2nd.html"><mo>2</mo> <mo>nd</mo></msup> $.
$s class ZZ>= $: <msub href="df-uz.html"><mi>&Zopf;</mi> <mo>&ge;</mo></msub> $.
$s class |_ $: <mfenced open="&lfloor;" close="&rfloor;" href="df-fl.html"><mi>.</mi></mfenced> $.
$s class |^ $: <mfenced open="&lceil;" close="&rceil;" href="df-ceil.html"><mi>.</mi></mfenced> $.
$s class Re $: <mo href="df-re.html">&Rfr;</mo> $.
$s class Im $: <mo href="df-im.html">&Ifr;</mo> $.
$s class * $: <mo href="df-cj.html">*</mo> $.
$s class gsum $: <msub href="df-gsum.html"><mo>&Sigma;</mo><mi>&#x1D454;</mi></msub> $.
$s class vol $: <mo href="df-vol.html">vol</mo> $.
$s class vol* $: <msup href="df-ovol.html"><mo>vol</mo> <mo>*</mo></msup> $.
$s class S.1 $: <msup href="df-itg1.html"><mo>&int;</mo> <mn>1</mn></msup> $.
$s class S.2 $: <msup href="df-itg2.html"><mo>&int;</mo> <mn>2</mn></msup> $.
$s class area $: <mo href="df-area.html">area</mo> $.

$( Operator Constants - usually not used outside definition $)
$s class +c $: <msub href="df-cda.html"> <mo>+</mo> <mo>c</mo> </msub> $.
$s class + $: <mo href="df-add.html">&plus;</mo> $.
$s class - $: <mo href="df-sub.html">&minus;</mo> $.
$s class / $: <mo href="df-div.html">&divide;</mo> $.
$s class x. $: <mo href="df-mul.html">&times;</mo> $.
$s class ^ $: <mo href="df-exp.html">^</mo> $.
$s class +e $: <msub href="df-xadd.html"><mo>&plus;</mo> <mi>&#x1D452;</mi></msub> $.
$s class -e A $: <mrow><msub href="df-xneg.html"><mo>&minus;</mo> <mi>&#x1D452;</mi></msub> #A </mrow> $.
$s class /e $: <msub href="df-xdiv.html"><mo>&divide;</mo> <mi>&#x1D452;</mi></msub> $.
$s class *e $: <msub href="df-xmul.html"><mo>&sdot;</mo> <mi>&#x1D452;</mi></msub> $.
$s class [,] $: <mfenced open='[' close=']' href="df-icc.html"><mi>.</mi></mfenced> $.
$s class [,) $: <mfenced open='[' close=')' href="df-ico.html"><mi>.</mi></mfenced> $.
$s class (,] $: <mfenced open='(' close=']' href="df-ioc.html"><mi>.</mi></mfenced> $.
$s class (,) $: <mfenced open='(' close=')' href="df-ioo.html"><mi>.</mi></mfenced> $.
$s class _C $: <mrow href="df-bc.html"> <mo>(</mo> <mfrac linethickness="0"><mi>.</mi> <mi>.</mi></mfrac><mo>)</mo> </mrow> $.
$s class _D $: <mi href="df-dv.html" mathvariant="normal">D</mi> $.
$s class sqrt $: <msqrt href="df-sqrt.html"><mi>.</mi></msqrt> $.
$s class ... $: <mo href="df-fz.html">&hellip;</mo> $.
$s class ..^ $: <mo href="df-fzo.html">..^</mo> $.
$s class -cn-> $: <munder accentunder href="df-cncf.html"><mo>&xrarr;</mo><mo>cn</mo></munder> $.
$s class mod $: <mo href="df-mod.html">mod</mo> $.
$s class +o $: <msub href="df-oadd.html"> <mo>+</mo> <mo>&#x1d45c;</mo> </msub> $.
$s class .o $: <msub href="df-omul.html"> <mo>&sdot;</mo> <mo>&#x1d45c;</mo> </msub> $.
$s class ^o $: <msub href="df-oexp.html"> <mo>&uarr;</mo> <mo>&#x1d45c;</mo> </msub> $.
$s class ^m $: <msub href="df-map.html"> <mo>&uarr;</mo> <mo>&#x1d45a;</mo> </msub> $.
$s class ^pm $: <msub href="df-pm.html"> <mo>&uarr;</mo> <mo>&#x1d45d;&#x1d45a;</mo> </msub> $.
$s class MblFn $: <mo href="df-mbf.html">MblFn</mo> $.
$s class limCC $: <msub href="df-limc.html"><mo>lim</mo> <mi>&Copf;</mi></msub> $.
$s class tX $: <msub href="df-tx.html"><mo>&times;</mo> <mi>t</mi></msub> $.

$s wff A R B $: <mrow>#A# #R# #B#</mrow> $.

$( By default, put brackets on infix operator classes $)
$s class ( A F B ) $: <mfenced><mrow>#A# #F# #B#</mrow></mfenced> $.

$( By default, don't put brackets on O-classes $)
$s class-o ( A F B ) $: <mrow>#A# #F# #B#</mrow> $.

$( In last resort, revert class-o to normal class (with parens) $)
$s class-o A $: #A# $.

$( Try displaying classes as numbers $)
$s class M $: <mn> #M# </mn> $.

$( For mmdefinitions.html exclusively ... does not work 
$s wff A = B $: <mrow> #A# <mo href="wceq.html">=</mo> #B# </mrow> $.
$s wff A e. B $: <mrow> #A# <mo href="wcel.html">&isin;</mo> #B# </mrow> $.
$s class ; A B $: <mrow> <mo>;</mo> #A# #B# </mrow> $. $)


$( ======================================================================= $)

$( Command: this is the command to be run by Metamath when outputting files
   for offline pre-rendering. The generated HTML/MATHML output is piped to
   the command's input stream, and the command's output stream is saved. $)
$c ../node_modules/mathjax-node-page/bin/mjpage --format MathML --output SVG --speech false --fontURL "http://metamath.tirix.org/fonts/HTML-CSS" --linebreaks $.


$( Container: this is what needs to be included around each formula. 
   The ### is replaced with the formula. It comes in two flavors, one diplay (block), and one for text (inline). $)
$d <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> ### </math> $.
$t <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> ### </math> $.
$( Header: this is what needs to be included in the HTML header $)
$h 
  <!-- Include the mm-web-ui javascript and stylesheet. -->
  <script src="mm-web-ui/externals/jquery.min.js" type="text/javascript"></script>
  <script src="mm-web-ui/mm-web-ui.js" type="text/javascript"></script>
	<link rel="stylesheet" type="text/css" href="mm-web-ui/mm-web-ui.css">
$.