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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">d</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">w</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">w'</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:25"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="incproj.html#R2">are_mutually_different</a> 
 <b>and </b><br/><a NAME="E2:25"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x'</font>,<font color="Maroon">y'</font>,<font color="Maroon">z'</font>,<font color="Maroon">w'</font>
 ;<br/>

<i><font color="Green">E41</font></i>: <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">x'</font>
<b>by </b><i>, , </i>
;<br/>
<i><font color="Green">E42</font></i>: <font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y'</font>
<b>by </b><i>, , </i>
;<br/>
<i><font color="Green">E43</font></i>: <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">z'</font>
<b>by </b><i>, , </i>
;<br/>
<font color="Maroon">w</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">w'</font>
<b>by </b><i>, , </i>
;<br/>
<b>hence </b><a NAME="E7:25"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y'</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z'</font> &amp; <font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w'</font> )
 <b>by </b><i>, , </i>;<br/>


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