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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k1</font>, <font color="Olive" title="b2">k2</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k1</font> &amp; <font color="Olive" title="b2">k2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font> holds <br/> <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">k1</font>,<font color="Olive" title="b2">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b1">k1</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">k1</font>, <font color="Maroon" title="c3">k2</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">k1</font> &amp; <font color="Maroon" title="c3">k2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font> implies  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E24">A5</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">k1</font> &amp; <font color="Maroon" title="c3">k2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">k11</font> = <font color="Maroon" title="c2">k1</font>, <font color="Maroon" title="c5">k21</font> = <font color="Maroon" title="c3">k2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:33"/><i><font color="Green" title="E25">A2</font></i>: 
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c5">k21</font></span>)</span> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#D3" target="_self" title="AFINSQ_2:def.3">AB540b</a></i>;<br/>
<a NAME="E4:33"/><i><font color="Green" title="E26">B2</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c5">k21</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k21</font>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T12" target="_self" title="AFINSQ_2:th.12">TH80</a>, <a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a></i>;<br/>
<a NAME="E5:33"/>
<font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E6:33"/><b>then </b>
<font color="Maroon" title="c2">k1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E7:33"/><b>then </b><i><font color="Green" title="E27">B43</font></i>: 
<font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">k1</font>
 
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:33_1"/>
( <font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k2</font> or <font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">k2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1"><b>suppose </b></a><a NAME="E1:33_1_1"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span><br/><div class="add"><a NAME="E2:33_1_1"/><i><font color="Green" title="E29">B9</font></i>: 
<font color="Maroon" title="c3">k2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E3:33_1_1"/><i><font color="Green" title="E30">B7</font></i>: 
<font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/><a NAME="E4:33_1_1"/>
<font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k2</font>
 <b>by </b><i><a class="txt" href="#E1:33_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="#E7:33"><i><font color="Green" title="E27">B43</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:33_1_1"/><b>then </b>
<font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:33_1_1"/><b>then </b><i><font color="Green" title="E31">B20</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T16" target="_self" title="AFINSQ_2:th.16">TH80b</a></i>;<br/><i><font color="Green" title="E32">B21</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">k1</font>
<b>by </b><i><a class="txt" href="#E2:33_1_1"><i><font color="Green" title="E29">B9</font></i></a>, <a class="txt" href="#E1:33_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>
<br/>.= 
<font color="Maroon" title="c3">k2</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span>

;<br/><a NAME="E8:33_1_1"/><b>then </b><i><font color="Green" title="E33">B30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:33_1_1"><i><font color="Green" title="E31">B20</font></i></a>, <a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="#E3:33_1_1"><i><font color="Green" title="E30">B7</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E9:33_1_1"/><b>then </b><i><font color="Green" title="E34">B5</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T12" target="_self" title="AFINSQ_2:th.12">TH80</a></i>;<br/><a NAME="E10:33_1_1"/>
<font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k11</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></i>;<br/><a NAME="E11:33_1_1"/><b>then </b>
<font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">k21</font>
 <b>by </b><i><a class="txt" href="#E1:33_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:33_1_1"/><b>then </b><i><font color="Green" title="E35">B3</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k21</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T16" target="_self" title="AFINSQ_2:th.16">TH80b</a>, <a class="txt" href="#E3:33"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="#E4:33"><i><font color="Green" title="E26">B2</font></i></a>, <a class="txt" href="#E3:33_1_1"><i><font color="Green" title="E30">B7</font></i></a></i>;<br/><a NAME="E13:33_1_1"/><b>then </b>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k21</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c4">k11</font>
 ;<br/><a NAME="E14:33_1_1"/><b>then </b><i><font color="Green" title="E36">B10</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E9:33_1_1"><i><font color="Green" title="E34">B5</font></i></a>, <a class="txt" href="#E2:33_1_1"><i><font color="Green" title="E29">B9</font></i></a>, <a class="txt" href="#E1:33_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E15:33_1_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> implies <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> )</span><br/>

<b>assume </b><a NAME="E1:33_1_1_2"/><i><font color="Green" title="E37">C2</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/>

<a NAME="E2:33_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">i</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">k21</font>
 
<b>by </b><i><a class="txt" href="#E12:33_1_1"><i><font color="Green" title="E35">B3</font></i></a>, <a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/>
<a NAME="E3:33_1_1_2"/><b>then </b><i><font color="Green" title="E38">C12</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c5">k21</font></span>)</span> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c5">k21</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:33"><i><font color="Green" title="E26">B2</font></i></a>, <a class="txt" href="#E3:33_1_1"><i><font color="Green" title="E30">B7</font></i></a>, <a class="ref" href="afinsq_2.html#T17" target="_self" title="AFINSQ_2:th.17">Th19b</a></i>;<br/>
<a NAME="E4:33_1_1_2"/>
<font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">k21</font>
 
<b>by </b><i><a class="txt" href="#E1:33_1_1_2"><i><font color="Green" title="E37">C2</font></i></a>, <a class="txt" href="#E12:33_1_1"><i><font color="Green" title="E35">B3</font></i></a>, <a class="txt" href="#E3:33_1_1"><i><font color="Green" title="E30">B7</font></i></a>, <a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/>
<a NAME="E5:33_1_1_2"/><b>then </b><i><font color="Green" title="E39">C40</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">k21</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/>
<a NAME="E6:33_1_1_2"/>
<font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k21</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k11</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:33_1_1_2"><i><font color="Green" title="E37">C2</font></i></a>, <a class="txt" href="#E12:33_1_1"><i><font color="Green" title="E35">B3</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:33_1_1_2"/><b>then </b><i><font color="Green" title="E40">C10</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="#E3:33_1_1"><i><font color="Green" title="E30">B7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:33_1_1_2"/><i><font color="Green" title="E41">C9</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font>
 
<b>by </b><i><a class="txt" href="#E1:33_1_1_2"><i><font color="Green" title="E37">C2</font></i></a>, <a class="txt" href="#E12:33_1_1"><i><font color="Green" title="E35">B3</font></i></a>, <a class="txt" href="#E7:33_1_1"><i><font color="Green" title="E32">B21</font></i></a>, <a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="ref" href="afinsq_2.html#T11" target="_self" title="AFINSQ_2:th.11">Th19</a>, <a class="txt" href="#E8:33_1_1_2"><i><font color="Green" title="E41">C9</font></i></a>, <a class="txt" href="#E8:33_1_1"><i><font color="Green" title="E33">B30</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="afinsq_2.html#T17" target="_self" title="AFINSQ_2:th.17">Th19b</a>, <a class="txt" href="#E7:33_1_1_2"><i><font color="Green" title="E40">C10</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E10:33_1_1_2"/>
<span class="p1">(<span class="default"><a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>by </b><i><a class="txt" href="#E5:33_1_1_2"><i><font color="Green" title="E39">C40</font></i></a>, <a class="ref" href="afinsq_2.html#T11" target="_self" title="AFINSQ_2:th.11">Th19</a>, <a class="txt" href="#E1:33"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="#E3:33"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="#E3:33_1_1_2"><i><font color="Green" title="E38">C12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E16:33_1_1"/>
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E14:33_1_1"><i><font color="Green" title="E36">B10</font></i></a>, <a class="ref" href="afinsq_1.html#T11" title="AFINSQ_1:th.11">AFINSQ_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_2"><b>suppose </b></a><a NAME="E1:33_1_2"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c2">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">k2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span></span><br/><div class="add"><a NAME="E2:33_1_2"/><b>then </b><i><font color="Green" title="E29">D3</font></i>: 
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="afinsq_2.html#T23" target="_self" title="AFINSQ_2:th.23">AB540f</a></i>;<br/><a NAME="E3:33_1_2"/>
<font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">k1</font>
 <b>by </b><i><a class="txt" href="#E1:33_1_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:33_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="nat_2.html#T10" title="NAT_2:th.10">NAT_2:10</a></i>;<br/><b>hence </b><a NAME="E5:33_1_2"/>
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k1</font>,<font color="Maroon" title="c3">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k1</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c2">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:33_1_2"><i><font color="Green" title="E29">D3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
