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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</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="E1:57"/><i><font color="Green" title="E44">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X</font>
 ;<br/>

<a NAME="E2:57"/><i><font color="Green" title="E45">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="waybel26.html#D5" target="_self" title="WAYBEL26:def.5">Def5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:57_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel26.html#K5" title="WAYBEL26:func.5">*graph</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span>
 ;<br/><a NAME="E2:57_1_1"/><b>then </b>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="txt" href="waybel26.html#E2:57"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="waybel26.html#T39" target="_self" title="WAYBEL26:th.39">Th39</a></i>;<br/><a NAME="E3:57_1_1"/><b>then </b>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="ref" href="waybel26.html#D5" target="_self" title="WAYBEL26:def.5">Def5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:57_1_1"/><i><font color="Green" title="E46">A3</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp; <font color="Maroon" title="c5">z</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"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="ref" href="relat_1.html#D13" title="RELAT_1:def.13">RELAT_1:def 13</a></i>;<br/><b>thus </b><a NAME="E6:57_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 <b>by </b><i><a class="txt" href="waybel26.html#E5:57_1_1"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:57_1"/><i><font color="Green" title="E46">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 ;<br/><a NAME="E3:57_1"/><b>then </b><i><font color="Green" title="E47">A5</font></i>: 
( <font color="Maroon" title="c3">x</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"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">W</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:57_1"/><b>then </b>
( <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 <b>by </b><i><a class="txt" href="waybel26.html#E1:57"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="waybel26.html#E2:57_1"><i><font color="Green" title="E46">A4</font></i></a>, <a class="ref" href="relat_1.html#D13" title="RELAT_1:def.13">RELAT_1:def 13</a></i>;<br/><a NAME="E5:57_1"/><b>then </b>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="ref" href="waybel26.html#D5" target="_self" title="WAYBEL26:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E6:57_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel26.html#K5" title="WAYBEL26:func.5">*graph</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span>
 <b>by </b><i><a class="txt" href="waybel26.html#E1:57"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="waybel26.html#E2:57"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="waybel26.html#E3:57_1"><i><font color="Green" title="E47">A5</font></i></a>, <a class="ref" href="waybel26.html#T39" target="_self" title="WAYBEL26:th.39">Th39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:57"/>
 <a href="waybel26.html#K5" title="WAYBEL26:func.5">*graph</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font>,<font color="Maroon" title="c2">X</font> <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">W</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</a></i>;<br/>


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