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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">S</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_1"/>
(  not <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> or <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1"><b>suppose </b></a><a NAME="E1:38_1_1"/>
not <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><div class="add"><a NAME="E2:38_1_1"/><b>then </b>
not <font color="Maroon">i</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">A</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/><b>hence </b><a NAME="E3:38_1_1"/>
<span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">A</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">S</font> is <a href="pencil_1.html#V16" target="_self">Segre-like</a>
 <b>by </b><i><a class="ref" href="funct_7.html#D3">FUNCT_7:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2"><b>suppose </b></a><a NAME="E1:38_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">i</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> ;<br/><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/><b>assume </b><a NAME="E3:38_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font>
 ;<br/><a NAME="E4:38_1_2"/>
<span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">A</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="pzfmisc1.html#D1">PZFMISC1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:38_1_2"/>
( not <span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">A</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is <a href="xboole_0.html#V1">empty</a> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">A</font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="polynom1.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is <a href="realset1.html#V1">trivial</a> )
 <b>by </b><i>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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