<?xml version="1.0"?>
<div class="add">

<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:28_1_1"/><i><font color="Green">E30</font></i>: 
( <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> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a></i>;<br/>
<a NAME="E3:28_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">v</font> = <font color="Maroon">x</font>, <font color="Maroon">w</font> = <font color="Maroon">y</font> as   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a><br/>

<b>take </b>
<font color="Maroon">y</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="complfld.html#K2">*'</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">w</font></span>)</span> <a href="complfld.html#K2">*'</a> 
 ;<br/><a NAME="E2:28_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">w</font></span>)</span> <a href="complfld.html#K2">*'</a> </span>)</span> <a href="complfld.html#K2">*'</a> 
 ;<br/><b>hence </b><a NAME="E3:28_1_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E6:28_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">w</font></span>)</span> <a href="complfld.html#K2">*'</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:28_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="relat_1.html#K1">K32</a>(<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span>) &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <a href="relat_1.html#K1">K32</a>(<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span>) &amp; not <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K1" target="_self">*'</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i>, , </i>;<br/>


</div>
