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<a NAME="E1:27_1_1"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:27_1_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">S</font> is <a href="funct_1.html#V3">constant</a>
 ;<br/><b>consider </b><font color="Maroon">n0</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>take </b><font color="Maroon">r</font> = <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n0</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>thus </b><a NAME="E3:27_1_1_1"/>
<font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">RNS</font><b> such that </b><a NAME="E3:27_1_1"/><i><font color="Green">E72</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 ;<br/>

<b>let </b><font color="Maroon">n1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">n2</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a><br/>

<b>assume </b><a NAME="E4:27_1_1"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">n1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">S</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">S</font> )
 ;<br/>

<b>hence </b><font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n1</font> = 
<font color="Maroon">r</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n2</font>
<b>by </b><i>, , </i>
;<br/><br/>


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