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<b>thus </b><a NAME="E1:37_1_1"/>
 <a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font> is <a href="funct_1.html#V3">constant</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E2:37_1_1_1"/><i><font color="Green">E19</font></i>: 
(  <a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="margrel1.html#K6">BOOLEAN</a>  )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E3:37_1_1_1"/>
for <font color="Olive">n1</font>, <font color="Olive">n2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> &amp; <font color="Olive">n2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1"><b>proof </b></a><div class="add">

<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> ;<br/>

<b>assume </b><a NAME="E1:37_1_1_1_1"/>
( <font color="Maroon">n1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">n1</font> = <font color="Maroon">n1</font>, <font color="Maroon">n2</font> = <font color="Maroon">n2</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> <b>by </b><i/>;<br/>
<a NAME="E3:37_1_1_1_1"/><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:37_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">n1</font>
 
;<br/>
<b>hence </b><a NAME="E5:37_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n2</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:37_1_1_1"/>
 <a href="bvfunc_1.html#K16" target="_self">O_el</a> <font color="Maroon">Y</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a></i>;<br/>


</div><b>end;</b></div>


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