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<span class="kw">let </span><font color="Maroon" title="c1">T</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds   <a href="fintopo3.html#K3" title="FINTOPO3:func.3">Fcl</a> <font color="Olive" title="b1">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="fintopo3.html#K3" title="FINTOPO3:func.3">Fcl</a> <font color="Maroon" title="c2">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span><br/>



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for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fintopo3.html#K2" title="FINTOPO3:func.2">Fcl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1 holds <br/><span class="p1">(<span class="default"><a href="fintopo3.html#K2" title="FINTOPO3:func.2">Fcl</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo3.html#D2" target="_self" title="FINTOPO3:def.2">Def2</a></span>;<br/>
<span class="kw">then </span> <a href="fintopo3.html#K3" title="FINTOPO3:func.3">Fcl</a> <font color="Maroon" title="c2">A</font>,2 = 
<span class="p1">(<span class="default"><a href="fintopo3.html#K3" title="FINTOPO3:func.3">Fcl</a> <font color="Maroon" title="c2">A</font>,1</span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo3.html#T15" target="_self" title="FINTOPO3:th.15">Th15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:19"/>
 <a href="fintopo3.html#K3" title="FINTOPO3:func.3">Fcl</a> <font color="Maroon" title="c2">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> </span>)</span> <a href="fin_topo.html#K9" title="FIN_TOPO:func.9">^b</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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