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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th23</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: ANPROJ_8:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span> holds  <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p0">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p5">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></span>)</span></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"><span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">q</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">r</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></span>)</span></div></div>
