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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th23</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: BKMODEL3:28</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span>  st <font color="Olive" title="b1">u</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Olive" title="b1">u</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b2">v</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> &amp; <font color="Olive" title="b2">v</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  &amp; <font color="Olive" title="b2">v</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; <font color="Olive" title="b3">w</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">w</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">w</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">w</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1</div></div>
