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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c4">G</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c2">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:64"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">T</font> #)
 <b>and </b><br/><a NAME="E2:64"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font>
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_2.html#D2" title="TOPS_2:def.2">TOPS_2:def 2</a><br/>

<b>assume </b><a NAME="E4:64"/><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">G</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">R</font> = <font color="Maroon" title="c5">P</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="waybel_9.html#E1:64"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/>
<a NAME="E6:64"/>
<font color="Maroon" title="c6">R</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="txt" href="waybel_9.html#E2:64"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="waybel_9.html#E3:64"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="waybel_9.html#E4:64"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="tops_2.html#D2" title="TOPS_2:def.2">TOPS_2:def 2</a></i>;<br/>
<a NAME="E7:64"/><b>then </b>
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c6">R</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a></i>;<br/>
<a NAME="E8:64"/><b>then </b>
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c6">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E9:64"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c6">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font>
 
;<br/>
<b>hence </b><a NAME="E10:64"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="waybel_9.html#E1:64"><i><font color="Green" title="E27">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a>,<a class="ref" href="pre_topc.html#D6" title="PRE_TOPC:def.6">PRE_TOPC:def 6</a><br/>


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