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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font> be   <a href="quaterni.html#V1" title="QUATERNI:attr.1">quaternion</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="quaterni.html#K32" title="QUATERNI:func.32">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K32" title="QUATERNI:func.32">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  iff <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font> )</span><br/>



<span class="kw">thus </span><a NAME="E1:139"/>
( <span class="p1"><a href="quaterni.html#K32" title="QUATERNI:func.32">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K32" title="QUATERNI:func.32">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="quaterni.html#E145"><span class="lab"><font color="Green" title="E79">Lm38</font></span></a>, <a class="ref" href="quaterni.html#T66" target="_self" title="QUATERNI:th.66">Th66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font> implies <span class="p1"><a href="quaterni.html#K32" title="QUATERNI:func.32">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K32" title="QUATERNI:func.32">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:139"/>
<font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="quaterni.html#K32" title="QUATERNI:func.32">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K32" title="QUATERNI:func.32">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:139"/>
<span class="p1"><a href="quaterni.html#K32" title="QUATERNI:func.32">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K32" title="QUATERNI:func.32">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="quaterni.html#E26"><span class="lab"><font color="Green" title="E20">Lm7</font></span></a>, <a class="txt" href="quaterni.html#E142"><span class="lab"><font color="Green" title="E76">Lm35</font></span></a>, <a class="ref" href="quaterni.html#T65" target="_self" title="QUATERNI:th.65">Th65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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