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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="Red">::  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>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font> holds <br/> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</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="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font> implies  <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> )</span><br/>



<span class="kw">assume </span><a NAME="E1:40"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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>,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></span><br/>

<span class="kw">thus </span> <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> = 
<font color="Maroon" title="c2">p</font> <a href="ordinal1.html#K2" title="ORDINAL1:func.2">|</a> <font color="Maroon" title="c1">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T25" target="_self" title="AFINSQ_2:th.25">Th25</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="afinsq_1.html#T56" title="AFINSQ_1:th.56">AFINSQ_1:56</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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