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<div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="midsp_3.html#NM3">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">W</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="midsp_3.html#NM3">Tuple</a> of <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">W</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:36_1_2"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">m</font> being   <a href="midsp_3.html#M1" target="_self">Nat</a> of <font color="Maroon">n</font> holds  <font color="Maroon">x</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="midsp_2.html#K9">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font></span>)</span>
 <b>and </b><br/><a NAME="E2:36_1_2"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">m</font> being   <a href="midsp_3.html#M1" target="_self">Nat</a> of <font color="Maroon">n</font> holds  <font color="Maroon">y</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="midsp_2.html#K9">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font></span>)</span>
 ;<br/>

<a NAME="E3:36_1_2"/>
for <font color="Olive">m</font> being   <a href="midsp_3.html#M1" target="_self">Nat</a> of <font color="Maroon">n</font> holds  <font color="Maroon">x</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Olive">m</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="midsp_3.html#M1" target="_self">Nat</a> of <font color="Maroon">n</font>;<br/>

<a NAME="E1:36_1_2_1"/>
<font color="Maroon">W</font> <a href="midsp_2.html#K9">.</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Maroon">m</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:36_1_2_1"/>
<font color="Maroon">x</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="midsp_3.html#K5" target="_self">.</a> <font color="Maroon">m</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:36_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/>


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