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<span class="kw">set </span><font color="Maroon" title="c1">Fa</font> = <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">F</font> = <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 as   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">F</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is  <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a>  &amp; <font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V2" title="LEXBFS:attr.2">iterative</a>  &amp; <font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V3" title="LEXBFS:attr.3">eventually-constant</a>  )</span><br/>

<a NAME="E2:24_1_1"/>
<font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c2">F</font> is  <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V2" title="LEXBFS:attr.2">iterative</a>  &amp; <font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V3" title="LEXBFS:attr.3">eventually-constant</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:24_1_1"/>
<font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V2" title="LEXBFS:attr.2">iterative</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V3" title="LEXBFS:attr.3">eventually-constant</a> </span><br/>

<a NAME="E5:24_1_1"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a>, <a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:24_1_1"/>
<font color="Maroon" title="c2">F</font> is  <a href="lexbfs.html#V3" title="LEXBFS:attr.3">eventually-constant</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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