<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th13</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: EUCLID13:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">An</font>, <font color="Olive" title="b3">Bn</font>, <font color="Olive" title="b4">Cn</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> <font color="Olive" title="b1">n</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b3">Bn</font>,<font color="Olive" title="b4">Cn</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b4">Cn</font>,<font color="Olive" title="b4">Cn</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2"><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|(</a><span class="default"><font color="Olive" title="b2">An</font>,<font color="Olive" title="b3">Bn</font></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></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">An</font>,<font color="Olive" title="b4">Cn</font></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"><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="b4">Cn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">An</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">Cn</font></span>)</span></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> &amp; <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="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">Cn</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">Cn</font></span>)</span></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="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="b4">Cn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">An</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">Cn</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"><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="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">Cn</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">Bn</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">An</font></span>)</span></span><a href="rvsum_1.html#K22" title="RVSUM_1:func.22">)|</a></span> )</div></div>
