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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">ThConv3</font></span>: <a NAME="T17"><span class="comment"><font color="firebrick">:: GTARSKI2:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <a href="gtarski2.html#K2" title="GTARSKI2:func.2">TarskiEuclid2Space</a> holds <br/> (  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gtarski2.html#K4" title="GTARSKI2:func.4">Tn2TR</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><a href="gtarski2.html#K4" title="GTARSKI2:func.4">Tn2TR</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gtarski2.html#K6" title="GTARSKI2:func.6">Tn2R</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p3">(<span class="default"><a href="gtarski2.html#K6" title="GTARSKI2:func.6">Tn2R</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> )</div></div>
