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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b> ex <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">A</font> );<br/>
<b>set </b><font color="Maroon" title="c2">B0</font> =  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>;<br/>
<a NAME="E1:76_1_1"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font></span>)</span> is <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>
 
;<br/>
<a NAME="E2:76_1_1"/><b>then </b><i><font color="Green" title="E40">A1</font></i>: 
 ex <font color="Olive" title="b1">A</font> being <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">A</font>]
 
;<br/>
<b>consider </b><font color="Maroon" title="c3">A</font> being  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E4:76_1_1"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">A</font>]
 <b>and </b><br/><a NAME="E5:76_1_1"/><i><font color="Green" title="E42">A3</font></i>: 
for <font color="Olive" title="b1">B</font> being <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">B</font>] holds <br/><font color="Maroon" title="c3">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">B</font>
 <b>from </b><i><a class="ref" href="ordinal1.html#S1" title="ORDINAL1:sch.1">ORDINAL1:sch 1</a>(<a class="txt" href="topgen_1.html#E2:76_1_1"><i><font color="Green" title="E40">A1</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon" title="c4">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E7:76_1_1"/><i><font color="Green" title="E43">A4</font></i>: 
( <font color="Maroon" title="c4">B1</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c4">B1</font> )
 <b>by </b><i><a class="txt" href="topgen_1.html#E4:76_1_1"><i><font color="Green" title="E41">A2</font></i></a></i>;<br/>
<b>take </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c4">B1</font>
;<br/>

<b>thus </b><a NAME="E8:76_1_1"/>
(  ex <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c4">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">A</font> ) &amp; ( for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">B</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> holds <br/> <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c4">B1</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">B</font> ) )
 <b>by </b><i><a class="txt" href="topgen_1.html#E5:76_1_1"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="topgen_1.html#E7:76_1_1"><i><font color="Green" title="E43">A4</font></i></a></i>;<br/>


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