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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: QUATERN3:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z1</font>, <font color="Olive" title="b2">z2</font>, <font color="Olive" title="b3">z</font> being   <a href="quaterni.html#NM1" title="QUATERNI:NM.1">Quaternion</a> holds  <span class="p1"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b1">z1</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><font color="Olive" title="b2">z2</font></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="quaterni.html#K24" title="QUATERNI:func.24">-</a> <font color="Olive" title="b3">z</font></span>)</span></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="quaterni.html#K27" title="QUATERNI:func.27">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">z</font> <a href="quaterni.html#K24" title="QUATERNI:func.24">-</a> <font color="Olive" title="b2">z2</font></span>)</span></span><a href="quaterni.html#K27" title="QUATERNI:func.27">.|</a></span></div></div>
