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<b>let </b><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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">FT</font> is <a href="fintopo6.html#V1" title="FINTOPO6:attr.1">connected</a> implies for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> &amp; <font color="Olive" title="b1">A</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> &amp; <font color="Olive" title="b2">B</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> holds <br/><font color="Olive" title="b1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">B</font> )</span><br/>

<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E22">A1</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font> is <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="fintopo6.html#D1" target="_self" title="FINTOPO6:def.1">FINTOPO6:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font>  st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> &amp; <font color="Olive" title="b1">A</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> &amp; <font color="Olive" title="b2">B</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> holds <br/><font color="Olive" title="b1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">B</font></span><br/>

<b>given </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FT</font><b> such that </b><a NAME="E3:43"/><i><font color="Green" title="E23">A2</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">FT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font>
 <b>and </b><br/><a NAME="E4:43"/><i><font color="Green" title="E24">A3</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> &amp; <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">FT</font> )
 <b>and </b><br/><a NAME="E5:43"/><i><font color="Green" title="E25">A4</font></i>: 
( <font color="Maroon" title="c2">A</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="fin_topo.html#V3" title="FIN_TOPO:attr.3">closed</a> &amp; <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">B</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>thus </b><a NAME="E6:43"/>
contradiction
 <b>by </b><i><a class="txt" href="fintopo6.html#E1:43"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="fintopo6.html#E3:43"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="fintopo6.html#E4:43"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="fintopo6.html#E5:43"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="fintopo6.html#T4" target="_self" title="FINTOPO6:th.4">Th4</a>, <a class="ref" href="fintopo6.html#T27" target="_self" title="FINTOPO6:th.27">Th27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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