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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#K5" title="FINTOPO3:func.5">Fint</a> <font color="Olive" title="b1">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a> </span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="fintopo3.html#K5" title="FINTOPO3:func.5">Fint</a> <font color="Maroon" title="c2">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a> </span><br/>



<a NAME="E1:21"/><i><font color="Green" title="E16">A1</font></i>: 
( ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <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">T</font>  st <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fintopo3.html#K4" title="FINTOPO3:func.4">Fint</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font> holds <br/><span class="p1">(<span class="default"><a href="fintopo3.html#K4" title="FINTOPO3:func.4">Fint</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"><font color="Olive" title="b1">n</font> <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="b2">B</font> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a>  ) &amp; <span class="p1">(<span class="default"><a href="fintopo3.html#K4" title="FINTOPO3:func.4">Fint</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="ref" href="fintopo3.html#D4" target="_self" title="FINTOPO3:def.4">Def4</a></i>;<br/>
<a NAME="E2:21"/>
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#K4" title="FINTOPO3:func.4">Fint</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><a href="fintopo3.html#K4" title="FINTOPO3:func.4">Fint</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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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#K8" title="FIN_TOPO:func.8">^i</a> 
 
<b>by </b><i><a class="ref" href="fintopo3.html#D4" target="_self" title="FINTOPO3:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
 <a href="fintopo3.html#K5" title="FINTOPO3:func.5">Fint</a> <font color="Maroon" title="c2">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="fin_topo.html#K8" title="FIN_TOPO:func.8">^i</a> 
 <b>by </b><i><a class="txt" href="fintopo3.html#E1:21"><i><font color="Green" title="E16">A1</font></i></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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