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<b>thus </b><a NAME="E1:16"/>
 <a href="jordan1h.html#K1" target="_self">RealOrd</a>  <a href="relat_2.html#R1">is_reflexive_in</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="jordan1h.html#E11"><i><font color="Green">Lemma4</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D8">ORDERS_1:def 8</a><br/>

<b>thus </b><a NAME="E2:16"/>
 <a href="jordan1h.html#K1" target="_self">RealOrd</a>  <a href="relat_2.html#R8">is_transitive_in</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="jordan1h.html#E13"><i><font color="Green">Lemma6</font></i></a></i>;<br/>

<b>thus </b><a NAME="E3:16"/>
 <a href="jordan1h.html#K1" target="_self">RealOrd</a>  <a href="relat_2.html#R4">is_antisymmetric_in</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="jordan1h.html#E12"><i><font color="Green">Lemma5</font></i></a></i>;<br/>

<b>thus </b><a NAME="E4:16"/>
 <a href="jordan1h.html#K1" target="_self">RealOrd</a>  <a href="relat_2.html#R6">is_connected_in</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="jordan1h.html#E14"><i><font color="Green">Lemma7</font></i></a></i>;<br/>


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