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<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K7">COMPLEMENT</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/><a NAME="E3:2_1_1"/>
<font color="Maroon">y</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i>, <a class="ref" href="setfam_1.html#D8">SETFAM_1:def 8</a></i>;<br/><b>then consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E5:2_1_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">y</font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">b</font>) &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i/>;<br/><a NAME="E6:2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">b</font>) <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">b</font>) <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a>  )
 ;<br/><b>hence </b><a NAME="E7:2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">F<sub>4</sub></font>(<font color="Olive">a</font>) <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() </span>}</span> 
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">F<sub>4</sub></font>(<font color="Olive">a</font>) <a href="subset_1.html#K3">`</a> </span>)</span> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E4:2_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">a</font>) <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() )
 ;<br/>
<a NAME="E5:2_1"/>
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">a</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K7">COMPLEMENT</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i>, <a class="ref" href="yellow_8.html#T14">YELLOW_8:14</a></i>;<br/>


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