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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th48</font></span>: <a NAME="T36"><span class="comment"><font color="firebrick">:: DIOPHAN2:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">c2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st  <a href="diophan2.html#K1" title="DIOPHAN2:func.1">ZeroPointSet</a> <span class="p1">(<span class="default"><a href="diophan2.html#K5" title="DIOPHAN2:func.5">LF</a> (<font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">c1</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> ex <font color="Olive" title="b7">x</font>, <font color="Olive" title="b8">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  st <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diophan2.html#K5" title="DIOPHAN2:func.5">LF</a> (<font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">c1</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b7">x</font>,<font color="Olive" title="b8">y</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diophan2.html#K5" title="DIOPHAN2:func.5">LF</a> (<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">c2</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b7">x</font>,<font color="Olive" title="b8">y</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">b2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">a2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">b1</font></span>)</span></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 4</div></div>
