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<a NAME="E1:92_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <font color="Maroon">F</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:92_1_1"/>
not  <a href="amistd_2.html#K10" target="_self">Shift</a> <font color="Maroon">F</font>,<font color="Maroon">k</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">f</font> =  <a href="amistd_2.html#K10" target="_self">Shift</a> <font color="Maroon">F</font>,<font color="Maroon">k</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E4:92_1_1"/>
not  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> is <a href="xboole_0.html#V1">empty</a>
 
;<br/>
<b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:92_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <font color="Maroon">F</font>,<font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E7:92_1_1"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Olive">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> &amp;  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:92_1_1"/>
contradiction
 ;<br/>


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