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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font>] <b>means </b>( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> holds <br/> ( <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) or  ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> st <br/>( <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; ( <font color="Maroon">a<sub>1</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> or <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) ) );<br/>
<b>set </b><font color="Maroon">CELL</font> = <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span> ;<br/>
<a NAME="E1:39_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">l</font>]
 
;<br/>
<a NAME="E2:39_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span> 
 
;<br/>
<a NAME="E3:39_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font>
 
<b>from </b><i><a class="ref" href="fraenkel.html#S10">FRAENKEL:sch 10</a>();<br/></i>
<b>hence </b><a NAME="E4:39_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font> : ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> holds <br/> ( <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">x</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; <font color="Olive">x</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) or  ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">d</font> st <br/>( <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> &amp; ( <font color="Olive">x</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> or <font color="Maroon">l</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">x</font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">i</font> ) ) ) </span>}</span>  is  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1">REAL</a> <font color="Maroon">d</font></span>)</span>
 <b>by </b><i/>;<br/>


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