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<div><span class="kw">theorem </span><a NAME="T82"><span class="comment"><font color="firebrick">:: EUCLID_8:82</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3 holds  <span class="p1"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Olive" title="b2">q</font></span>)</span></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b1">p</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b2">q</font>,<font color="Olive" title="b2">q</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T138" onmouseover="rs('rvsum_1/T138')" onmouseout="rh()">RVSUM_1:138</a></span>;<br/></div></div>
