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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:71"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font>
 <b>and </b><br/><a NAME="E2:71"/><i><font color="Green" title="E33">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 ;<br/>

<a NAME="E3:71"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</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><br/>

<b>assume </b><a NAME="E1:71_1"/><i><font color="Green" title="E34">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E2:71_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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="c3">f</font>
 
<b>by </b><i><a class="txt" href="partfun1.html#E1:71"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:71_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span>
 <b>by </b><i><a class="txt" href="partfun1.html#E1:71"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="partfun1.html#E2:71"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="partfun1.html#E1:71_1"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="partfun1.html#T78" target="_self" title="PARTFUN1:th.78">Th78</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:71"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="partfun1.html#D4" target="_self" title="PARTFUN1:def.4">PARTFUN1:def 4</a><br/>


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