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<a NAME="E1:37"/>
 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  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <a href="gtarski2.html#K2" title="GTARSKI2:func.2">TarskiEuclid2Space</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span><br/>

<a NAME="E1:37_1"/>
 <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="metric_1.html#K3" title="METRIC_1:func.3">dist</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E2:37_1"/>
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski1.html#D15" onmouseover="rs('gtarski1/D15')" onmouseout="rh()">GTARSKI1:def 15</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:37"/>
 <a href="gtarski2.html#K2" title="GTARSKI2:func.2">TarskiEuclid2Space</a>  is  <a href="gtarski1.html#V2" title="GTARSKI1:attr.2">satisfying_CongruenceSymmetry</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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