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<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:36"/>
( <font color="Maroon">p</font> <a href="finseq_4.html#R2" target="_self">just_once_values</a> <font color="Maroon">x</font> implies ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:36_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="finseq_4.html#R2" target="_self">just_once_values</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:36_1"/><b>then </b>
<font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="finseq_4.html#K1" target="_self">&lt;-</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:36_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, , </i>;<br/>


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

<b>assume </b><b>that </b><br/><a NAME="E2:36"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E4:36"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> )
 
<b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:36_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E2:36_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> <a href="finseq_4.html#K5" target="_self">..</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E3:36_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E4:36_2"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_4.html#D1" target="_self">Def1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E5:36_2"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p</font> <a href="relat_1.html#K10">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/><b>hence </b><a NAME="E6:36_2"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon">p</font> <a href="finseq_4.html#R2" target="_self">just_once_values</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/>


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