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<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D15">PBOOLE:def 15</a><br/>

<b>assume </b><a NAME="E1:66_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>assume </b><a NAME="E2:66_1_1"/>
not <span class="p1">(<span class="default"><a href="closure1.html#K6" target="_self">MSFixPoints</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:66_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="closure1.html#K6" target="_self">MSFixPoints</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E6:66_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, , </i>;<br/>
<a NAME="E7:66_1_1"/>
<font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="pboole.html#D15">PBOOLE:def 15</a></i>;<br/>
<a NAME="E8:66_1_1"/><b>then </b>
<font color="Maroon">f</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="xboole_0.html#K1">{}</a> , <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , <a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<b>hence </b><a NAME="E9:66_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="partfun1.html#T54">PARTFUN1:54</a></i>;<br/>


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