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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>;<br/>



<b>set </b><font color="Maroon" title="c3">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> ;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:7_1"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c5">P</font> = <font color="Maroon" title="c4">x</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> ;<br/><a NAME="E3:7_1"/>
( <font color="Maroon" title="c5">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> )
 <b>by </b><i><a class="txt" href="yellow_9.html#E1:7_1"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="setfam_1.html#D8" title="SETFAM_1:def.8">SETFAM_1:def 8</a></i>;<br/><b>hence </b><a NAME="E4:7_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> 
 ;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:7"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> 
 ;<br/>

<a NAME="E3:7"/><b>then </b>
 ex <font color="Olive" title="b1">P</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp; <font color="Olive" title="b1">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> )
 
;<br/>
<b>hence </b><a NAME="E4:7"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K7" title="SETFAM_1:func.7">COMPLEMENT</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="ref" href="yellow_8.html#T14" title="YELLOW_8:th.14">YELLOW_8:14</a></i>;<br/>


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