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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:5"/><i><font color="Green">E4</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>1</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</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>2</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>

<b>assume </b><a NAME="E2:5"/><i><font color="Green">E5</font></i>: 
<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="E3:5"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 ;<br/>

<a NAME="E4:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="tsp_1.html#V1">T_0</a>
 
<b>by </b><i><a class="ref" href="tsp_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E5:5"/><b>then </b><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="tsp_1.html#V1">T_0</a>
 
<b>by </b><i><a class="txt" href="tsp_2.html#E1:5"><i><font color="Green">E4</font></i></a>, <a class="txt" href="tsp_2.html#E2:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="tsp_1.html#T5">TSP_1:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>assume </b><a NAME="E1:5_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="tsp_1.html#V1">T_0</a>
 ;<br/><b>assume </b><a NAME="E2:5_1"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <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_2.html#E1:5"><i><font color="Green">E4</font></i></a></i>;<br/><a NAME="E4:5_1"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="tsp_1.html#V1">T_0</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="tsp_2.html#E1:5"><i><font color="Green">E4</font></i></a>, <a class="txt" href="tsp_2.html#E2:5"><i><font color="Green">E5</font></i></a>, <a class="txt" href="tsp_2.html#E1:5_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="tsp_2.html#E2:5_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="tsp_1.html#T5">TSP_1:5</a></i>;<br/><b>hence </b><a NAME="E5:5_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="tsp_2.html#E2:5"><i><font color="Green">E5</font></i></a>, <a class="txt" href="tsp_2.html#E3:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="tsp_2.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:5"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 <b>by </b><i><a class="txt" href="tsp_2.html#E5:5"><i><font color="Green">E7</font></i></a>, <a class="ref" href="tsp_2.html#D4" target="_self">Def4</a></i>;<br/>


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