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<b>let </b><font color="Maroon">z1</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">z2</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:137"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:137"/><i><font color="Green">E40</font></i>: 
(  <a href="quaterni.html#K17" target="_self">Rea</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span> &amp;  <a href="quaterni.html#K18" target="_self">Im1</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span> &amp;  <a href="quaterni.html#K19" target="_self">Im2</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span> &amp;  <a href="quaterni.html#K20" target="_self">Im3</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="quaterni.html#E19"><i><font color="Green">Lemma75</font></i></a></i>;<br/>
<a NAME="E3:137"/>
(  <a href="quaterni.html#K17" target="_self">Rea</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="quaterni.html#K18" target="_self">Im1</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="quaterni.html#K19" target="_self">Im2</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="quaterni.html#K20" target="_self">Im3</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K29" target="_self">-</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E4:137"/>
<font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font>
 <b>by </b><i>, </i>;<br/>


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