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<b>let </b><font color="Maroon">IT1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">IT2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:86_1_2_1"/>
<font color="Maroon">F</font> is <a href="glib_000.html#V13" target="_self">halting</a>
 ;<br/><b>assume </b><a NAME="E2:86_1_2_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">IT1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Maroon">IT1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> ) )
 ;<br/><b>assume </b><a NAME="E3:86_1_2_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">IT2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">IT2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Maroon">IT2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> ) )
 ;<br/><a NAME="E4:86_1_2_1"/>
( <font color="Maroon">IT1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">IT2</font> &amp; <font color="Maroon">IT2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">IT1</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:86_1_2_1"/>
<font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:86_1_2"/>
( not <font color="Maroon">F</font> is <a href="glib_000.html#V13" target="_self">halting</a> &amp; <font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">IT2</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font> )
 ;<br/>


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