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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>assume </b><a NAME="E1:90"/><i><font color="Green">E41</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<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>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="yellow_9.html#M3" target="_self">Refinement</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>

<i><font color="Green">E42</font></i>: the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="yellow_9.html#D6" target="_self">Def6</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="yellow_9.html#E1:90"><i><font color="Green">E41</font></i></a></i>
;<br/>
<a NAME="E3:90"/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:90"/><b>then </b>
( the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="cantor_1.html#D5">CANTOR_1:def 5</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:90"/><b>then </b>
( the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:90"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="yellow_9.html#M2" target="_self">TopExtension</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is    <a href="yellow_9.html#M2" target="_self">TopExtension</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_9.html#E1:90"><i><font color="Green">E41</font></i></a>, <a class="txt" href="yellow_9.html#E2:90"><i><font color="Green">E42</font></i></a>, <a class="ref" href="yellow_9.html#D5" target="_self">Def5</a></i>;<br/>


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