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<b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>;<br/>
<b>consider </b><font color="Maroon">B</font> being    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>
<b>take </b><font color="Maroon">C</font> = <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">i</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>;<br/>

<b>thus </b><a NAME="E3:42_1_1"/>
<font color="Maroon">C</font> is <a href="pencil_1.html#V16" target="_self">Segre-like</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">i</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D20" target="_self">PENCIL_1:def 20</a><br/>

<b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>;<br/>

<a NAME="E1:42_1_1_1"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 
;<br/>
<a NAME="E2:42_1_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:42_1_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
not <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/>
<b>assume </b><a NAME="E4:42_1_1_1"/>
<font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">i</font>
 ;<br/>

<a NAME="E5:42_1_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/>
<a NAME="E6:42_1_1_1"/><b>then </b>
<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:42_1_1_1"/>
( not <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is <a href="realset1.html#V1">trivial</a> )
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:42_1_1"/>
not <font color="Maroon">C</font> is <a href="pencil_1.html#V13" target="_self">trivial-yielding</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1_2"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">S</font> = <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D16" target="_self">PENCIL_1:def 16</a><br/>

<a NAME="E1:42_1_1_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:42_1_1_2"/>
<font color="Maroon">S</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>

<a NAME="E3:42_1_1_2"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">B</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:42_1_1_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/>
<a NAME="E5:42_1_1_2"/>
( 0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> &amp; 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E6:42_1_1_2"/><b>then </b>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:42_1_1_2"/>
not <font color="Maroon">S</font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>


</div>
