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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</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> is  <a href="orders_5.html#V2" title="ORDERS_5:attr.2">strongly_connected</a>  implies ( <font color="Maroon" title="c1">A</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp; <font color="Maroon" title="c1">A</font> is  <a href="orders_5.html#V1" title="ORDERS_5:attr.1">connected</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c1">A</font> is  <a href="orders_5.html#V2" title="ORDERS_5:attr.2">strongly_connected</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> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp; <font color="Maroon" title="c1">A</font> is  <a href="orders_5.html#V1" title="ORDERS_5:attr.1">connected</a>  )</span><br/>

<a NAME="E2:31_1_1"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> holds <br/><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="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>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="relat_2.html#D7" onmouseover="rs('relat_2/D7')" onmouseout="rh()">RELAT_2:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:31_1_1"/>
<font color="Maroon" title="c1">A</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D1" onmouseover="rs('relat_2/D1')" onmouseout="rh()">RELAT_2:def 1</a>, <a class="ref" href="orders_2.html#D2" onmouseover="rs('orders_2/D2')" onmouseout="rh()">ORDERS_2:def 2</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"> <font color="Maroon" title="c1">A</font> is  <a href="orders_5.html#V1" title="ORDERS_5:attr.1">connected</a> </span><br/>

<a NAME="E4:31_1_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">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</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>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">A</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>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="relat_2.html#D7" onmouseover="rs('relat_2/D7')" onmouseout="rh()">RELAT_2:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:31_1_1"/>
<font color="Maroon" title="c1">A</font> is  <a href="orders_5.html#V1" title="ORDERS_5:attr.1">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D6" onmouseover="rs('relat_2/D6')" onmouseout="rh()">RELAT_2:def 6</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/>


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