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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: EUCLID_8:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">y1</font>, <font color="Olive" title="b5">y2</font>, <font color="Olive" title="b6">y3</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds  <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><font color="Olive" title="b4">y1</font>,<font color="Olive" title="b5">y2</font>,<font color="Olive" title="b6">y3</font></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">y1</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">x2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b5">y2</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">x3</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b6">y3</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span></div></div>
