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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:112_1_1_1"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>
 ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E2:112_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font>
 ;<br/><a NAME="E3:112_1_1_1"/><b>then </b>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" target="_self" title="FUNCT_1:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E4:112_1_1_1"/>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="funct_1.html#E1:112_1_1_1"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="relat_1.html#T184" title="RELAT_1:th.184">RELAT_1:184</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:112_1_1"/><i><font color="Green" title="E45">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font> holds <br/><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">s</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="relat_1.html#D15" title="RELAT_1:def.15">RELAT_1:def 15</a><br/>

<b>assume </b><a NAME="E3:112_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 ;<br/>

<a NAME="E4:112_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5" target="_self" title="FUNCT_1:def.5">Def5</a></i>;<br/>
<a NAME="E5:112_1_1"/><b>then </b>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="funct_1.html#E2:112_1_1"><i><font color="Green" title="E45">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:112_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


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