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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E10</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> #)
 ;<br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V2" target="_self">proper</a>
 ;<br/>

<a NAME="E3:29"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="tex_2.html#V1" target="_self">proper</a>
 
<b>by </b><i><a class="txt" href="tex_2.html#E1:29"><i><font color="Green">E10</font></i></a>, <a class="ref" href="tex_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:29"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V2" target="_self">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D3" target="_self">Def3</a></i>;<br/>


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