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<span class="kw">let </span><font color="Maroon" title="c1">FT</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <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">  for <font color="Olive" title="b1">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Olive" title="b1">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  holds <br/><font color="Olive" title="b1">C</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>; <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">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  implies <font color="Maroon" title="c2">C</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
( <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Maroon" title="c1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  )
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c2">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">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="c2">C</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> </span><br/>

<a NAME="E3:45"/>
<font color="Maroon" title="c2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">C</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="fin_topo.html#T13" onmouseover="rs('fin_topo/T13')" onmouseout="rh()">FIN_TOPO:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:45"/>
<font color="Maroon" title="c2">C</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a>  is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="fintopo6.html#T35" target="_self" onmouseover="rs('fintopo6/T35')" onmouseout="rh()">Th34</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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