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<b>let </b><font color="Maroon" title="c1">h1</font>, <font color="Maroon" title="c2">h2</font> be   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1"><b>suppose </b></a><a NAME="E1:41_1_1"/><i><font color="Green" title="E26">A0</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">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_1"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1_1"/><i><font color="Green" title="E27">A71</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c3">g1</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:41_1_1_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> &amp; <font color="Maroon" title="c1">h1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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">h1</font> holds <br/><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> ) &amp;  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font></span>)</span> <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#D4" target="_self" title="AFINSQ_2:def.4">AC300</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_1_1_1"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_1"/><i><font color="Green" title="E29">A72</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c4">g2</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:41_1_1_1_1_1_1"/><i><font color="Green" title="E30">A2</font></i>: 
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">g2</font> &amp; <font color="Maroon" title="c2">h2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c2">h2</font> holds <br/><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></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">h2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> ) &amp;  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span> <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#D4" target="_self" title="AFINSQ_2:def.4">AC300</a></i>;<br/><b>set </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon" title="c6">g2b</font> = <font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span>;<br/><a NAME="E4:41_1_1_1_1_1_1"/><i><font color="Green" title="E31">E4b</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="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></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> <font color="Maroon" title="c4">g2</font> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">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> <font color="Maroon" title="c4">g2</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_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"><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <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#T6" target="_self" title="AFINSQ_2:th.6">AC500</a></i>;<br/><b>set </b><font color="Maroon" title="c7">g4</font> = <font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>;<br/><i><font color="Green" title="E32">E10</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">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c4">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>
;<br/><i><font color="Green" title="E33">E34</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<font color="Maroon" title="c1">h1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="afinsq_2.html#T7" target="_self" title="AFINSQ_2:th.7">AE359</a>, <a class="txt" href="#E1:41_1_1_1_1"><i><font color="Green" title="E27">A71</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="afinsq_2.html#T7" target="_self" title="AFINSQ_2:th.7">AE359</a>, <a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1"><i><font color="Green" title="E27">A71</font></i></a></i>
;<br/><a NAME="E7:41_1_1_1_1_1_1"/><i><font color="Green" title="E34">E93</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">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></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="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>;<br/><i><font color="Green" title="E35">E94</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">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span>
<b>by </b><i><a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>
;<br/><a NAME="E9:41_1_1_1_1_1_1"/><i><font color="Green" title="E36">E95</font></i>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</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"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:41_1_1_1_1_1_1"><i><font color="Green" title="E34">E93</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1"><i><font color="Green" title="E29">A72</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E10:41_1_1_1_1_1_1"/><i><font color="Green" title="E37">E35</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1_1_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">i</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"> ( <font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:41_1_1_1_1_1_1_4"/><i><font color="Green" title="E38">G1</font></i>: 
<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">i0</font> = <font color="Maroon" title="c8">i</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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_1_1_1_1_4_1"/>
( <font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c3">g1</font> or <font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1_4_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_1_4_1_1"/><i><font color="Green" title="E39">H0</font></i>: 
<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c3">g1</font>
 ; <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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_1_1_1_1_1_4_1_1"/><b>then </b><i><font color="Green" title="E40">G2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T7" target="_self" title="AFINSQ_2:th.7">AE359</a></i>;<br/><a NAME="E3:41_1_1_1_1_1_1_4_1_1"/>
<font color="Maroon" title="c8">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">i</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="E4:41_1_1_1_1_1_1_4_1_1"/><b>then </b>
<font color="Maroon" title="c8">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> <font color="Maroon" title="c3">g1</font>
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_1"><i><font color="Green" title="E39">H0</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:41_1_1_1_1_1_1_4_1_1"/><b>then </b><i><font color="Green" title="E41">G4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T7" target="_self" title="AFINSQ_2:th.7">AE359</a></i>;<br/><a NAME="E6:41_1_1_1_1_1_1_4_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">h1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T7" target="_self" title="AFINSQ_2:th.7">AE359</a>, <a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_1"><i><font color="Green" title="E39">H0</font></i></a></i>;<br/><b>hence </b><a NAME="E7:41_1_1_1_1_1_1_4_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:41_1_1_1_1_1_1_4_1_1"><i><font color="Green" title="E40">G2</font></i></a>, <a class="txt" href="#E5:41_1_1_1_1_1_1_4_1_1"><i><font color="Green" title="E41">G4</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_1"><i><font color="Green" title="E39">H0</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1_4_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_1_4_1_2"/><i><font color="Green" title="E39">H0</font></i>: 
<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font>
 ; <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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1_4_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_1_1_1_1_4_1_2_1"/>
( <font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> or <font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> )
 </span><b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2"><i><font color="Green" title="E39">H0</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_1_4_1_2_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_1_4_1_2_1_1"/><i><font color="Green" title="E40">J0</font></i>: 
<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font>
 ; <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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_1_1_1_1_1_4_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c8">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font>
 <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="E3:41_1_1_1_1_1_1_4_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c8">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">i</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c10">i1</font> = <font color="Maroon" title="c8">i</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> 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>  ;<br/><a NAME="E5:41_1_1_1_1_1_1_4_1_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">i</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> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4"><i><font color="Green" title="E38">G1</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E6:41_1_1_1_1_1_1_4_1_2_1_1"/><b>then </b><i><font color="Green" title="E41">G1en</font></i>: 
<font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>;<br/><a NAME="E7:41_1_1_1_1_1_1_4_1_2_1_1"/>
<font color="Maroon" title="c10">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="E8:41_1_1_1_1_1_1_4_1_2_1_1"/><b>then </b><i><font color="Green" title="E42">G3</font></i>: 
<font color="Maroon" title="c10">i1</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"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E6:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E41">G1en</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E9:41_1_1_1_1_1_1_4_1_2_1_1"/><i><font color="Green" title="E43">G5p</font></i>: 
<font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">i0</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> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/><a NAME="E10:41_1_1_1_1_1_1_4_1_2_1_1"/>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">i0</font> &amp; <font color="Maroon" title="c9">i0</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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E40">J0</font></i></a>, <a class="txt" href="#E8:41_1_1_1_1_1_1"><i><font color="Green" title="E35">E94</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4"><i><font color="Green" title="E38">G1</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:41_1_1_1_1_1_1_4_1_2_1_1"/><b>then </b><i><font color="Green" title="E44">G4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c9">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">i1</font>
 <b>by </b><i><a class="ref" href="afinsq_1.html#T22" title="AFINSQ_1:th.22">AFINSQ_1:22</a></i>;<br/><a NAME="E12:41_1_1_1_1_1_1_4_1_2_1_1"/><i><font color="Green" title="E45">G5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">h2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E9:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E43">G5p</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2"><i><font color="Green" title="E39">H0</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4"><i><font color="Green" title="E38">G1</font></i></a>, <a class="ref" href="afinsq_1.html#T22" title="AFINSQ_1:th.22">AFINSQ_1:22</a></i>;<br/><a NAME="E13:41_1_1_1_1_1_1_4_1_2_1_1"/><i><font color="Green" title="E46">G51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">i1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <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="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E8:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E42">G3</font></i></a></i>;<br/><a NAME="E14:41_1_1_1_1_1_1_4_1_2_1_1"/><i><font color="Green" title="E47">G52</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <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="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E6:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E41">G1en</font></i></a></i>;<br/><a NAME="E15:41_1_1_1_1_1_1_4_1_2_1_1"/>
<font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">i1</font></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">h2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E6:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E41">G1en</font></i></a></i>;<br/><b>hence </b><a NAME="E16:41_1_1_1_1_1_1_4_1_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E9:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E43">G5p</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2"><i><font color="Green" title="E39">H0</font></i></a>, <a class="txt" href="#E8:41_1_1_1_1_1_1"><i><font color="Green" title="E35">E94</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1_4"><i><font color="Green" title="E38">G1</font></i></a>, <a class="txt" href="#E11:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E44">G4</font></i></a>, <a class="txt" href="#E12:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E45">G5</font></i></a>, <a class="txt" href="#E13:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E46">G51</font></i></a>, <a class="txt" href="#E14:41_1_1_1_1_1_1_4_1_2_1_1"><i><font color="Green" title="E47">G52</font></i></a>, <a class="ref" href="afinsq_1.html#T22" title="AFINSQ_1:th.22">AFINSQ_1:22</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="41_1_1_1_1_1_1_4_1_2_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_1_4_1_2_1_2"/><i><font color="Green" title="E40">H0</font></i>: 
<font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font>
 ; <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"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_1_1_1_1_1_4_1_2_1_2"/><b>then </b><i><font color="Green" title="E41">H8</font></i>: 
<font color="Maroon" title="c8">i</font> <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="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 <b>by </b><i><a class="ref" href="nat_d.html#T34" title="NAT_D:th.34">NAT_D:34</a></i>;<br/><a NAME="E3:41_1_1_1_1_1_1_4_1_2_1_2"/><i><font color="Green" title="E42">G2r</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1"><i><font color="Green" title="E29">A72</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/><i><font color="Green" title="E43">G2</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E40">H0</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E3:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E42">G2r</font></i></a>, <a class="ref" href="afinsq_1.html#D4" title="AFINSQ_1:def.4">AFINSQ_1:def 4</a></i>
;<br/><a NAME="E5:41_1_1_1_1_1_1_4_1_2_1_2"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c3">g1</font>
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1"><i><font color="Green" title="E27">A71</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E6:41_1_1_1_1_1_1_4_1_2_1_2"/><b>then </b><i><font color="Green" title="E44">G34</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <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="c3">g1</font></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#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/><a NAME="E7:41_1_1_1_1_1_1_4_1_2_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="E8:41_1_1_1_1_1_1_4_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <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>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E9:41_1_1_1_1_1_1_4_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c3">g1</font>
 <b>by </b><i><a class="txt" href="#E6:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E44">G34</font></i></a>, <a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/><a NAME="E10:41_1_1_1_1_1_1_4_1_2_1_2"/><b>then </b><i><font color="Green" title="E45">G4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E2:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E41">H8</font></i></a>, <a class="ref" href="afinsq_1.html#D4" title="AFINSQ_1:def.4">AFINSQ_1:def 4</a></i>;<br/><a NAME="E11:41_1_1_1_1_1_1_4_1_2_1_2"/><i><font color="Green" title="E46">G65</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</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">h1</font></span>)</span> <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="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/><a NAME="E12:41_1_1_1_1_1_1_4_1_2_1_2"/>
<font color="Maroon" title="c2">h2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E1:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E40">H0</font></i></a>, <a class="txt" href="#E11:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E46">G65</font></i></a>, <a class="txt" href="#E9:41_1_1_1_1_1_1"><i><font color="Green" title="E36">E95</font></i></a>, <a class="ref" href="afinsq_1.html#T22" title="AFINSQ_1:th.22">AFINSQ_1:22</a></i>;<br/><b>hence </b><a NAME="E13:41_1_1_1_1_1_1_4_1_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E43">G2</font></i></a>, <a class="txt" href="#E10:41_1_1_1_1_1_1_4_1_2_1_2"><i><font color="Green" title="E45">G4</font></i></a>, <a class="ref" href="afinsq_2.html#T6" target="_self" title="AFINSQ_2:th.6">AC500</a>, <a class="txt" href="#E1:41_1_1_1_1_1_1"><i><font color="Green" title="E29">A72</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</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><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E11:41_1_1_1_1_1_1"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="#E1:41_1_1"><i><font color="Green" title="E26">A0</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E12:41_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E38">R50</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>;<br/><a NAME="E13:41_1_1_1_1_1_1"/><i><font color="Green" title="E39">R4n</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="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E1:41_1_1_1_1_1_1"><i><font color="Green" title="E29">A72</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E14:41_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E40">R4</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></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#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/><i><font color="Green" title="E41">R2</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
<b>by </b><i><a class="txt" href="#E12:41_1_1_1_1_1_1"><i><font color="Green" title="E38">R50</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="#E13:41_1_1_1_1_1_1"><i><font color="Green" title="E39">R4n</font></i></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>
;<br/><a NAME="E16:41_1_1_1_1_1_1"/><i><font color="Green" title="E42">R7n</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <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>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <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="E17:41_1_1_1_1_1_1"/><i><font color="Green" title="E43">R3</font></i>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E14:41_1_1_1_1_1_1"><i><font color="Green" title="E40">R4</font></i></a>, <a class="txt" href="#E16:41_1_1_1_1_1_1"><i><font color="Green" title="E42">R7n</font></i></a>, <a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/><a NAME="E18:41_1_1_1_1_1_1"/><i><font color="Green" title="E44">R5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E7:41_1_1_1_1_1_1"><i><font color="Green" title="E34">E93</font></i></a>, <a class="txt" href="#E15:41_1_1_1_1_1_1"><i><font color="Green" title="E41">R2</font></i></a>, <a class="txt" href="#E17:41_1_1_1_1_1_1"><i><font color="Green" title="E43">R3</font></i></a>, <a class="ref" href="afinsq_1.html#D4" title="AFINSQ_1:def.4">AFINSQ_1:def 4</a></i>;<br/><a NAME="E19:41_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</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="c4">g2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span> <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"><font color="Maroon" title="c4">g2</font> <a href="afinsq_2.html#K1" title="AFINSQ_2:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">g1</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E14:41_1_1_1_1_1_1"><i><font color="Green" title="E40">R4</font></i></a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></i>;<br/><b>hence </b><a NAME="E20:41_1_1_1_1_1_1"/>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="ref" href="afinsq_2.html#D4" target="_self" title="AFINSQ_2:def.4">AC300</a>, <a class="txt" href="#E5:41_1_1_1_1_1_1"><i><font color="Green" title="E32">E10</font></i></a>, <a class="txt" href="#E6:41_1_1_1_1_1_1"><i><font color="Green" title="E33">E34</font></i></a>, <a class="txt" href="#E10:41_1_1_1_1_1_1"><i><font color="Green" title="E37">E35</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E3:41_1_1_1_1_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="#E18:41_1_1_1_1_1_1"><i><font color="Green" title="E44">R5</font></i></a>, <a class="txt" href="#E4:41_1_1_1_1_1_1"><i><font color="Green" title="E31">E4b</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_1_1_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E29">A73</font></i>: 
<font color="Maroon" title="c2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:41_1_1_1_1_1_2"/><b>then </b>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><b>hence </b><a NAME="E4:41_1_1_1_1_1_2"/>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:41_1_1_1_1_1_2"><i><font color="Green" title="E29">A73</font></i></a>, <a class="ref" href="afinsq_1.html#T32" title="AFINSQ_1:th.32">AFINSQ_1:32</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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_1_1_2"/><b>then </b><i><font color="Green" title="E27">A73</font></i>: 
<font color="Maroon" title="c1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:41_1_1_1_2"/><b>then </b>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><b>hence </b><a NAME="E4:41_1_1_1_2"/>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:41_1_1_1_2"><i><font color="Green" title="E27">A73</font></i></a>, <a class="ref" href="afinsq_1.html#T32" title="AFINSQ_1:th.32">AFINSQ_1:32</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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2"><b>suppose </b></a><a NAME="E1:41_1_2"/><i><font color="Green" title="E26">A0</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">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span></span><br/><div class="add"><a NAME="E2:41_1_2"/><b>then </b><i><font color="Green" title="E27">A80n</font></i>: 
<font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:41_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c1">h1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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">h1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E4:41_1_2"/><b>then </b>
<font color="Maroon" title="c1">h1</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="txt" href="#E1:41_1_2"><i><font color="Green" title="E26">A0</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>;<br/><a NAME="E5:41_1_2"/><b>then </b><i><font color="Green" title="E28">A81</font></i>: 
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><a NAME="E6:41_1_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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">h1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E7:41_1_2"/><b>then </b>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">h2</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="txt" href="#E1:41_1_2"><i><font color="Green" title="E26">A0</font></i></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></i>;<br/><b>hence </b><a NAME="E8:41_1_2"/>
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h1</font> <a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">^</a> <font color="Maroon" title="c2">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c1">h1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">Sum</a> <font color="Maroon" title="c2">h2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:41_1_2"><i><font color="Green" title="E27">A80n</font></i></a>, <a class="txt" href="#E5:41_1_2"><i><font color="Green" title="E28">A81</font></i></a>, <a class="ref" href="afinsq_1.html#T18" title="AFINSQ_1:th.18">AFINSQ_1:18</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>

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