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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>thus </b><a NAME="E1:28"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3" target="_self">`</a>  )
 <b>by </b><i><a class="ref" href="xboole_1.html#T34">XBOOLE_1:34</a></i>;<br/>

<i><font color="Green">E7</font></i>: <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6" target="_self">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3" target="_self">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3" target="_self">`</a> </span>)</span> <a href="subset_1.html#K3" target="_self">`</a> 

<br/>.= 
<font color="Maroon">c<sub>2</sub></font>

;<br/>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6" target="_self">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3" target="_self">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3" target="_self">`</a> </span>)</span> <a href="subset_1.html#K3" target="_self">`</a> 

<br/>.= 
<font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>hence </b><a NAME="E4:28"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3" target="_self">`</a>  implies <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="subset_1.html#E2:28"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xboole_1.html#T34">XBOOLE_1:34</a></i>;<br/>


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