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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">ThEquiv</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: GTARSKI2:12</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">p</font>, <font color="Olive" title="b3">q</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="gtarski2.html#K1" title="GTARSKI2:func.1">TarskiEuclidSpace</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b4">p1</font>, <font color="Olive" title="b5">q1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p1</font> &amp; <font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q1</font> holds <br/>(  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid.html#K13" title="EUCLID:func.13">Pitag_dist</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">p1</font>,<font color="Olive" title="b5">q1</font>) &amp;  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</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"><font color="Olive" title="b4">p1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">q1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> )</div></div>
