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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">Y0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:117"/>
<font color="Maroon">A</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y0</font>
 ;<br/>

<a NAME="E2:117"/><b>then </b>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 
;<br/>
<a NAME="E3:117"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#NK6" target="_self">Sspace</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 
<b>by </b><i><a class="ref" href="tex_4.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E4:117"/>
 <a href="tex_4.html#NK6" target="_self">Sspace</a> <font color="Maroon">A</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y0</font>
 <b>by </b><i><a class="ref" href="tex_4.html#D7" target="_self">Def7</a></i>;<br/>


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