<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th37</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: BORSUK_7:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</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><br/>  for <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</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#K14" title="EUCLID:func.14">Euclid</a> 3</span>)</span>  st <font color="Olive" title="b3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p1</font> &amp; <font color="Olive" title="b4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p2</font> holds <br/><span class="p1">(<span class="default"><a href="euclid.html#K13" title="EUCLID:func.13">Pitag_dist</a> 3</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K3" title="SQUARE_1:func.3">sqrt</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"><font color="Olive" title="b1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Olive" title="b2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a></span>)</span></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></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">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Olive" title="b2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a></span>)</span></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a></span>)</span></span>)</span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span></div></div>
