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<b>let </b><font color="Maroon">Gs</font> be    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:82"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">Gs</font> is <a href="lexbfs.html#V10" target="_self">eventually-constant</a>
 ;<br/>

<b>consider </b><font color="Maroon">n</font> being  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:82"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">m</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">m</font> holds <br/><font color="Maroon">Gs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Gs</font> <a href="funct_1.html#K1">.</a> <font color="Olive">m</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E4:82"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E5:82"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">Gs</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Gs</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:82"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E6:82"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E7:82"/>
<font color="Maroon">Gs</font> is <a href="glib_000.html#V13">halting</a>
 <b>by </b><i>, <a class="ref" href="glib_000.html#D56">GLIB_000:def 56</a></i>;<br/>


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