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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>

<b>assume </b><a NAME="E1:30"/>
<font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V7" title="RELAT_2:attr.7">strongly_connected</a>
 ;<br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R7" title="RELAT_2:pred.7">is_strongly_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D15" target="_self" title="RELAT_2:def.15">Def15</a></i>;<br/>
<b>thus </b><a NAME="E3:30"/>
<font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<a NAME="E1:30_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">R</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="relat_2.html#E2:30"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="relat_2.html#D7" target="_self" title="RELAT_2:def.7">Def7</a></i>;<br/>
<a NAME="E2:30_1"/><b>then </b>
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D6" target="_self" title="RELAT_2:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E3:30_1"/>
<font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D14" target="_self" title="RELAT_2:def.14">Def14</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:30"/>
<font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D1" target="_self" title="RELAT_2:def.1">RELAT_2:def 1</a>,<a class="ref" href="relat_2.html#D9" target="_self" title="RELAT_2:def.9">RELAT_2:def 9</a><br/>

<b>assume </b><a NAME="E1:30_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 ;<br/>

<b>hence </b><a NAME="E2:30_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="relat_2.html#E2:30"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="relat_2.html#D7" target="_self" title="RELAT_2:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div>


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