<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">a</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>





<b>set </b><font color="Maroon" title="c4">fd</font> =  <a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>;<br/>
<b>set </b><font color="Maroon" title="c5">fm</font> =  <a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( <span class="p1">(<span class="default"><a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">$1 <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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  );<br/>
<a NAME="E1:26"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1"/>
<span class="p1">(<span class="default"><a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E2:26_1"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="ref" href="real_3.html#T12" target="_self" title="REAL_3:th.12">Th12</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>;<br/>
<a NAME="E3:26_1"/><i><font color="Green" title="E23">A3</font></i>: 
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="ref" href="real_3.html#D2" target="_self" title="REAL_3:def.2">Def2</a></i>;<br/>
<b>assume </b><a NAME="E4:26_1"/><i><font color="Green" title="E24">A4</font></i>: 
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E5:26_1"/><b>then </b><i><font color="Green" title="E25">A5</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="real_3.html#E3:26_1"><i><font color="Green" title="E23">A3</font></i></a></i>;<br/>
<a NAME="E6:26_1"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_d.html#T2" title="NAT_D:th.2">NAT_D:2</a></i>;<br/>
<a NAME="E7:26_1"/><b>then </b><i><font color="Green" title="E26">A6</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="real_3.html#E2:26_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="real_3.html#E3:26_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="real_3.html#E5:26_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="nat_d.html#T1" title="NAT_D:th.1">NAT_D:1</a></i>;<br/>
<a NAME="E8:26_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="real_3.html#E4:26_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="real_3.html#D2" target="_self" title="REAL_3:def.2">Def2</a></i>;<br/>
<a NAME="E9:26_1"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<a NAME="E10:26_1"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 
;<br/>
<b>hence </b><a NAME="E11:26_1"/>
contradiction
 <b>by </b><i><a class="txt" href="real_3.html#E7:26_1"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="nat_d.html#T1" title="NAT_D:th.1">NAT_D:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:26"/><i><font color="Green" title="E22">A7</font></i>: 
for <font color="Olive" title="b1">b</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">b</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">b</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:26_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">b</font>]
 ;<br/>

<b>assume </b><a NAME="E2:26_2"/>
<span class="p1">(<span class="default"><a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E3:26_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E4:26_2"/><b>then </b><i><font color="Green" title="E23">A8</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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="ref" href="real_3.html#D3" target="_self" title="REAL_3:def.3">Def3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">x</font> = <span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<b>assume </b><a NAME="E5:26_2"/><i><font color="Green" title="E24">A9</font></i>: 
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E6:26_2"/><b>then </b><i><font color="Green" title="E25">A10</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E7:26_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K3" title="NAT_1:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></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"><span class="p3">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_d.html#T2" title="NAT_D:th.2">NAT_D:2</a></i>;<br/>
<a NAME="E8:26_2"/><b>then </b><i><font color="Green" title="E26">A11</font></i>: 
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="real_3.html#E4:26_2"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="real_3.html#E6:26_2"><i><font color="Green" title="E25">A10</font></i></a>, <a class="ref" href="nat_d.html#T1" title="NAT_D:th.1">NAT_D:1</a></i>;<br/>
<a NAME="E9:26_2"/><i><font color="Green" title="E27">A12</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">b</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#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E10:26_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="real_3.html#E5:26_2"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="real_3.html#T14" target="_self" title="REAL_3:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E11:26_2"/>
contradiction
 <b>by </b><i><a class="txt" href="real_3.html#E8:26_2"><i><font color="Green" title="E26">A11</font></i></a>, <a class="txt" href="real_3.html#E9:26_2"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="real_3.html#T15" target="_self" title="REAL_3:th.15">Th15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:26"/>
for <font color="Olive" title="b1">b</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">b</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="real_3.html#E1:26"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="real_3.html#E2:26"><i><font color="Green" title="E22">A7</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:26"/>
( <span class="p1">(<span class="default"><a href="real_3.html#K2" title="REAL_3:func.2">divSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="real_3.html#K1" title="REAL_3:func.1">modSeq</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>


</div>
