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<b>let </b><font color="Maroon">r</font> be  non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">o</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" target="_self">Tdisk</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="brouwer.html#K2" target="_self">Tdisk</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>;<br/>





<a NAME="E1:24"/>
<font color="Maroon">f</font> <a href="abian.html#R3">has_a_fixpoint</a> 
 
<b>by </b><i/>;<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="E3:24"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">x</font> <a href="abian.html#R1">is_a_fixpoint_of</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="abian.html#D5">ABIAN:def 5</a></i>;<br/>
<b>take </b>
<font color="Maroon">x</font>
;<br/>

<a NAME="E4:24"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="abian.html#D3">ABIAN:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">x</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" target="_self">Tdisk</a> <font color="Maroon">o</font>,<font color="Maroon">r</font></span>)</span>
 ;<br/>

<b>thus </b><a NAME="E6:24"/>
<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>, <a class="ref" href="abian.html#D3">ABIAN:def 3</a></i>;<br/>


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