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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X0</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 ;<br/>

<b>hence </b><a NAME="E2:38"/>
( <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a> implies <font color="Maroon" title="c3">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a> )
 <b>by </b><i><a class="ref" href="tex_3.html#D3" target="_self" title="TEX_3:def.3">Def3</a></i>;<br/>

<b>assume </b><a NAME="E3:38"/>
<font color="Maroon" title="c3">A</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 ;<br/>

<a NAME="E4:38"/><b>then </b>
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">X</font>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> holds <br/><font color="Olive" title="b1">B</font> is <a href="tops_1.html#V2" title="TOPS_1:attr.2">boundary</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E1:38"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V3" title="TEX_3:attr.3">boundary</a>
 <b>by </b><i><a class="ref" href="tex_3.html#D3" target="_self" title="TEX_3:def.3">Def3</a></i>;<br/>


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