OpenMath

OpenMath is an extensible standard for representing the semantics of mathematical objects.

https://openmath.github.io

OpenMath Signatures

Type System: sts
Content Dictionary: set1
CD Signature File: set1.sts

official 
               
Date:  1999-04-13
Author: David Carlisle

cartesian_product 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
  <OMA>
    <OMS cd="sts" name="mapsto"/>
    <OMA>
      <OMS cd="sts" name="nary"/>
      <OMA>
        <OMS cd="sts" name="structure"/>
	<OMV name="Set"/>
      </OMA>
    </OMA>
    <OMA>
      <OMS cd="sts" name="structure"/>
      <OMV name="Set1"/>
    </OMA>
  </OMA>
</OMOBJ>
( ( Set * ) >> Set1 )

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map 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
  <OMS cd="sts" name="mapsto"/>
    <OMA>
      <OMS cd="sts" name="mapsto"/>
      <OMS cd="sts" name="Object"/>
      <OMS cd="sts" name="Object"/>
    </OMA>
    <OMV name="Set"/>
    <OMV name="Set"/>
 </OMA>
</OMOBJ>
( ( Object >> Object ) Set >> Set )

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suchthat 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
  <OMS cd="sts" name="mapsto"/>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMV name="Set"/>
    </OMA>
    <OMA>
      <OMS name="mapsto" cd="sts"/>
      <OMV name="Set"/>
      <OMS name="Boolean" cd="setname2"/>
    </OMA>
    <OMA>
      <OMS name="structure" cd="sts"/>
      <OMV name="Set"/>
    </OMA>
 </OMA>
</OMOBJ>
( Set ( Set >> Boolean ) >> Set )

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emptyset 

 <OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
   <OMV name="Set"/>
 </OMOBJ>
Set

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size 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="CardinalNumber"/>
 </OMA>
</OMOBJ>
( Set >> CardinalNumber )

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set 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
  <OMS name="mapsto" cd="sts"/>
   <OMA>
    <OMS name="nary" cd="sts"/>
     <OMS name="Object" cd="sts"/>
   </OMA>
  <OMV name="Set"/>
 </OMA>
</OMOBJ>
( ( Object * ) >> Set )

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intersect 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMA>
     <OMS name="nassoc" cd="sts"/>
     <OMV name="Set"/>
    </OMA>
    <OMV name="Set"/>
 </OMA>
</OMOBJ>
( ( Set *assoc ) >> Set )

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union 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMA>
     <OMS name="nassoc" cd="sts"/>
     <OMV name="Set"/>
    </OMA>
    <OMV name="Set"/>
 </OMA>
</OMOBJ>
( ( Set *assoc ) >> Set )

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setdiff 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
 </OMA>
</OMOBJ>
( Set Set >> Set )

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subset 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Set Set >> Boolean )

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in 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMS name="Object" cd="sts"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Object Set >> Boolean )

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notin 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMS name="Object" cd="sts"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Object Set >> Boolean )

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prsubset 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Set Set >> Boolean )

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notsubset 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Set Set >> Boolean )

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notprsubset 

<OMOBJ xmlns="http://www.openmath.org/OpenMath"> 
 <OMA>
   <OMS name="mapsto" cd="sts"/>
    <OMV name="Set"/>
    <OMV name="Set"/>
    <OMS cd="setname2" name="Boolean"/>
 </OMA>
</OMOBJ>
( Set Set >> Boolean )

Content Dictionary Entry.

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