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<b>set </b><font color="Maroon">c</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>set </b><font color="Maroon">r</font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>set </b><font color="Maroon">Z</font> = <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span> ;<br/>
<a NAME="E1:23_1"/><i><font color="Green">E30</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<b>from </b><i><a class="ref" href="domain_1.html#S7">DOMAIN_1:sch 7</a>();<br/></i>
<a NAME="E2:23_1"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">Z</font> = <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i/>;<br/>
<a NAME="E4:23_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="wellord1.html#R1">is_well_founded_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:23_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="wellord1.html#K1">-Seg</a> <font color="Maroon">a</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Z</font> )
 <b>by </b><i><a class="ref" href="wellord1.html#D3">WELLORD1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<a NAME="E8:23_1"/>
 ex <font color="Olive">a'</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a'</font>] )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:23_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>]
 ;<br/>

<b>given </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><a NAME="E10:23_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">y</font>] &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">a</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">F<sub>1</sub></font>() )
 ;<br/>

<a NAME="E11:23_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="wellord1.html#K1">-Seg</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="wellord1.html#D1">WELLORD1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:23_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


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