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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1" target="_self">TopStruct</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #);<br/>
<b>thus </b><a NAME="E1:20"/>
 <a href="pre_topc.html#K2" target="_self">[#]</a> <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D9" target="_self">PRE_TOPC:def 9</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #);<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>thus </b><a NAME="E3:20_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:20_1"><i><font color="Green">E11</font></i></a></i>;<br/><b>thus </b><a NAME="E4:20_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)</span>)</span>
 <b>by </b><i><a class="ref" href="pre_topc.html#T15" target="_self">Th15</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E3:20"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)</span>)</span> )
 ;<br/>

<b>thus </b><a NAME="E4:20"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <a href="pre_topc.html#G1" target="_self">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" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #)
 <b>by </b><i><a class="txt" href="pre_topc.html#E3:20"><i><font color="Green">E11</font></i></a>, <a class="ref" href="pre_topc.html#T15" target="_self">Th15</a></i>;<br/>


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