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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="t_0topsp.html#V2">V117</a>  <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>5</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="tsp_1.html#E30"><i><font color="Green">Lemma23</font></i></a></i>;<br/>
<a NAME="E2:39"/><i><font color="Green">E26</font></i>: 
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
;<br/>
<b>assume </b><a NAME="E3:39"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:39"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="tsp_1.html#E2:39"><i><font color="Green">E26</font></i></a>, <a class="ref" href="pre_topc.html#D9">PRE_TOPC:def 9</a></i>;<br/>
<a NAME="E5:39"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 
<b>by </b><i><a class="ref" href="tsp_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 
<b>by </b><i><a class="txt" href="tsp_1.html#E4:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="tsp_1.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i><a class="ref" href="tsp_1.html#T15" target="_self">Th15</a></i>;<br/>


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