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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K2" target="_self">meet</a> <font color="Maroon">F</font>
 ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E2:11_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><a NAME="E3:11_1"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>hence </b><a NAME="E4:11_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">z</font>
 <b>by </b><i>, <a class="ref" href="funct_6.html#T37">FUNCT_6:37</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:11"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">z</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="prob_1.html#K1">.</a> <font color="Olive">z</font>
 ;<br/>

<a NAME="E3:11"/>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:11"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K2" target="_self">meet</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="funct_6.html#T37">FUNCT_6:37</a></i>;<br/>


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