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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a> holds   <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Olive" title="b1">p</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Olive" title="b1">p</font>,1,<font color="Maroon" title="c1">k</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Maroon" title="c2">p</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Maroon" title="c2">p</font>,1,<font color="Maroon" title="c1">k</font>)</span><br/>



<a NAME="E1:32"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_2.html#T8" title="NAT_2:th.8">NAT_2:8</a></span>;<br/>
<a NAME="E2:32"/>
 <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Maroon" title="c2">p</font>,1,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T16" target="_self" title="AFINSQ_2:th.16">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:32"/>
 <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Maroon" title="c2">p</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K3" title="AFINSQ_2:func.3">mid</a> (<font color="Maroon" title="c2">p</font>,1,<font color="Maroon" title="c1">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="afinsq_2.html#T10" target="_self" title="AFINSQ_2:th.10">Th19</a></span>; <a class="txt" 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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