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<b>let </b><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a><br/>

<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c14">i1</font>, <font color="Maroon" title="c15">i2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:17"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c14">i1</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>  &amp; <font color="Maroon" title="c15">i2</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>  )
 <b>and </b><br/><a NAME="E4:17"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="ami_3.html#K15" title="AMI_3:func.15">--&gt;</a> <font color="Maroon" title="c14">i1</font>,<font color="Maroon" title="c15">i2</font>
 <b>by </b><i><a class="ref" href="ami_4.html#T11" target="_self" title="AMI_4:th.11">Th11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">s</font> = <font color="Maroon" title="c13">x</font> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">p</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon" title="c18">q</font> =  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> ;<br/>
<a NAME="E6:17"/><i><font color="Green" title="E18">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<a NAME="E7:17"/><b>then </b><i><font color="Green" title="E19">A4</font></i>: 
(  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E8:17"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E9:17"/><b>then </b><i><font color="Green" title="E20">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th4</a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<div><i><font color="Green" title="E21">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c19">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:17_1"/><i><font color="Green" title="E22">A7</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> &amp; <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/><a NAME="E4:17_1"/><i><font color="Green" title="E23">A8</font></i>: 
(  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 )
 <b>by </b><i><a class="ref" href="ami_3.html#T56" title="AMI_3:th.56">AMI_3:56</a></i>;<br/><a NAME="E5:17_1"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E9:17"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="ami_4.html#E3:17_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E6:17_1"/><b>then </b><i><font color="Green" title="E24">A9</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 )
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E7:17_1"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 )
 <b>by </b><i><a class="txt" href="ami_4.html#E6:17"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="ami_4.html#E3:17_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:17_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="ami_4.html#E6:17_1"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="ami_3.html#T57" title="AMI_3:th.57">AMI_3:57</a></i>;<br/></div><b>end;</b></div>
<a NAME="E11:17"/><b>then </b><i><font color="Green" title="E22">A10</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<a NAME="E12:17"/>
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E13:17"/><b>then </b><i><font color="Green" title="E23">A11</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E11:17"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E14:17"/><i><font color="Green" title="E24">A12</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_2"/><i><font color="Green" title="E25">A13</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E11:17"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/>
<a NAME="E2:17_2"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:17_2"/><b>then </b><i><font color="Green" title="E26">A14</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E9:17"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:17_2"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font></span>)</span> <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="ami_4.html#E10:17"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:17_2"/><b>then </b><i><font color="Green" title="E27">A15</font></i>: 
not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E3:17_2"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>thus </b><a NAME="E6:17_2"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E1:17_2"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="ami_4.html#E3:17_2"><i><font color="Green" title="E26">A14</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D44" title="AMI_1:def.44">AMI_1:def 44</a><br/>

<a NAME="E7:17_2"/>
(  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 &amp;  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 &amp;  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 &amp;  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 )
 
<b>by </b><i><a class="ref" href="ami_3.html#T57" title="AMI_3:th.57">AMI_3:57</a></i>;<br/>
<a NAME="E8:17_2"/><b>then </b><i><font color="Green" title="E28">A16</font></i>: 
not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th4</a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>thus </b> <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E1:17_2"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="ami_4.html#E3:17_2"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="ami_1.html#D43" title="AMI_1:def.43">AMI_1:def 43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E5:17_2"><i><font color="Green" title="E27">A15</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E8:17_2"><i><font color="Green" title="E28">A16</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon" title="c16">s</font>
;<br/>

<b>thus </b><a NAME="E15:17"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</font>
 ;<br/>

<a NAME="E16:17"/><i><font color="Green" title="E25">A17</font></i>: 
for <font color="Olive" title="b1">t</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>   st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">t</font> holds <br/>( <font color="Olive" title="b1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> &amp; <font color="Olive" title="b1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">t</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:17_3"/><i><font color="Green" title="E26">A18</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 ;<br/>

<a NAME="E2:17_3"/>
<font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E3:17_3"/><b>then </b><i><font color="Green" title="E27">A19</font></i>: 
<font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E1:17_3"><i><font color="Green" title="E26">A18</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<font color="Maroon" title="c16">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E7:17"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c14">i1</font>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="ami_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> = 
<font color="Maroon" title="c16">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E7:17"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="ami_4.html#E3:17_3"><i><font color="Green" title="E27">A19</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c15">i2</font>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E17:17"/><i><font color="Green" title="E26">A20</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">s1</font>, <font color="Maroon" title="c20">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25" title="AMI_1:def.25">AMI_1:def 25</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:17_4"/><i><font color="Green" title="E27">A21</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">s1</font>
 <b>and </b><br/><a NAME="E2:17_4"/><i><font color="Green" title="E28">A22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">s2</font>
 ;<br/>

<a NAME="E3:17_4"/><i><font color="Green" title="E29">A23</font></i>: 
<font color="Maroon" title="c19">s1</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="ami_4.html#E14:17"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4"><i><font color="Green" title="E27">A21</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E4:17_4"/><i><font color="Green" title="E30">A24</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">s1</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E13:17"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4"><i><font color="Green" title="E27">A21</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:17_4"/><i><font color="Green" title="E31">A25</font></i>: 
<font color="Maroon" title="c20">s2</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="ami_4.html#E14:17"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4"><i><font color="Green" title="E28">A22</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E6:17_4"/><i><font color="Green" title="E32">A26</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">s2</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E13:17"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4"><i><font color="Green" title="E28">A22</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:17_4"/><i><font color="Green" title="E33">A27</font></i>: 
( <font color="Maroon" title="c20">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> &amp; <font color="Maroon" title="c20">s2</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E16:17"><i><font color="Green" title="E25">A17</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4"><i><font color="Green" title="E28">A22</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c21">A</font> = <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c22">C</font> = <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>;<br/>
<i><font color="Green" title="E34">A28</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="ami_4.html#E9:17"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T42" title="ENUMSET1:th.42">ENUMSET1:42</a></i>
;<br/>
<b>let </b><font color="Maroon" title="c23">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>set </b><font color="Maroon" title="c24">Cs</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font>;<br/>
<b>set </b><font color="Maroon" title="c25">Cs2</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font>;<br/>
<a NAME="E9:17_4"/><i><font color="Green" title="E35">A29</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="ref" href="ami_1.html#T86" title="AMI_1:th.86">AMI_1:86</a></i>;<br/>
<a NAME="E10:17_4"/>
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="ref" href="ami_1.html#T86" title="AMI_1:th.86">AMI_1:86</a></i>;<br/>
<b>then </b><i><font color="Green" title="E36">A30</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> = 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> 
<b>by </b><i><a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th4</a>, <a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4</span>)</span></span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
<b>by </b><i><a class="txt" href="ami_4.html#E9:17_4"><i><font color="Green" title="E35">A29</font></i></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th4</a>, <a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a></i>
;<br/>
<i><font color="Green" title="E37">A31</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>
<br/>.= 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>
;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <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>means </b>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> $1</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> );<br/>
<a NAME="E13:17_4"/><i><font color="Green" title="E38">A32</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_4"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_4"/><i><font color="Green" title="E39">A33</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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="c19">s1</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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="c20">s2</font> )
 
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c19">s1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="ami_4.html#E3:17_4"><i><font color="Green" title="E29">A23</font></i></a>, <a class="ref" href="ami_1.html#D41" title="AMI_1:def.41">AMI_1:def 41</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c20">s2</font>
<b>by </b><i><a class="txt" href="ami_4.html#E5:17_4"><i><font color="Green" title="E31">A25</font></i></a>, <a class="ref" href="ami_1.html#D41" title="AMI_1:def.41">AMI_1:def 41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
;<br/>

<b>thus </b><a NAME="E3:17_4_4"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E16:17"><i><font color="Green" title="E25">A17</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4"><i><font color="Green" title="E27">A21</font></i></a>, <a class="txt" href="ami_4.html#E7:17_4"><i><font color="Green" title="E33">A27</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_4"><i><font color="Green" title="E39">A33</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:17_4"/><i><font color="Green" title="E39">A34</font></i>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>2</sub></font>[4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">i</font>] &amp; <font color="Olive" title="b2">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 holds <br/><font color="Maroon">S<sub>2</sub></font>[<span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b2">j</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c26">i</font>, <font color="Maroon" title="c27">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:17_4_5"/><i><font color="Green" title="E40">A35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:17_4_5"/><i><font color="Green" title="E41">A36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:17_4_5"/><i><font color="Green" title="E42">A37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
 ;<br/>

<b>assume </b><a NAME="E4:17_4_5"/>
( <font color="Maroon" title="c27">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c27">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 )
 ;<br/>

<a NAME="E5:17_4_5"/><b>then </b><i><font color="Green" title="E43">A38</font></i>: 
( <font color="Maroon" title="c27">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c27">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c27">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c27">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T29" title="NAT_1:th.29">NAT_1:29</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_4_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_4_5_1"/>
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 )
 </span><b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E5:17_4"><i><font color="Green" title="E31">A25</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E7:17_4"><i><font color="Green" title="E33">A27</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green" title="E9">Lm3</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_4_5_1_1"><b>suppose </b></a><a NAME="E1:17_4_5_1_1"/><i><font color="Green" title="E44">A39</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:17_4_5_1_1"/><i><font color="Green" title="E45">A40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <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">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E3:17_4_5_1_1"/><i><font color="Green" title="E46">A41</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <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">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E4:17_4_5_1_1"/><i><font color="Green" title="E47">A42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <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">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E5:17_4_5_1_1"/><i><font color="Green" title="E48">A43</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="ami_4.html#E1:17_4_5"><i><font color="Green" title="E40">A35</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_1"><i><font color="Green" title="E44">A39</font></i></a></i>;<br/><a NAME="E6:17_4_5_1_1"/><b>then </b><i><font color="Green" title="E49">A44</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <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="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1 )
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_1"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>;<br/><i><font color="Green" title="E50">A45</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E5:17_4_5_1_1"><i><font color="Green" title="E48">A43</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_1"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
;<br/><i><font color="Green" title="E51">A46</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E5:17_4_5_1_1"><i><font color="Green" title="E48">A43</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_1"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
;<br/><i><font color="Green" title="E52">A47</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E5:17_4_5_1_1"><i><font color="Green" title="E48">A43</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5"><i><font color="Green" title="E42">A37</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_1"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>
;<br/><a NAME="E10:17_4_5_1_1"/><i><font color="Green" title="E53">A48</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 2 )
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>;<br/><i><font color="Green" title="E54">A49</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="txt" href="ami_4.html#E7:17_4_5_1_1"><i><font color="Green" title="E50">A45</font></i></a>, <a class="txt" href="ami_4.html#E8:17_4_5_1_1"><i><font color="Green" title="E51">A46</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
;<br/><i><font color="Green" title="E55">A50</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="txt" href="ami_4.html#E7:17_4_5_1_1"><i><font color="Green" title="E50">A45</font></i></a>, <a class="txt" href="ami_4.html#E8:17_4_5_1_1"><i><font color="Green" title="E51">A46</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
;<br/><i><font color="Green" title="E56">A51</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5_1_1"><i><font color="Green" title="E45">A40</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="txt" href="ami_4.html#E9:17_4_5_1_1"><i><font color="Green" title="E52">A47</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>
;<br/><a NAME="E14:17_4_5_1_1"/><i><font color="Green" title="E57">A52</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 3 )
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5_1_1"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>;<br/><i><font color="Green" title="E58">A53</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5_1_1"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5_1_1"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="txt" href="ami_4.html#E13:17_4_5_1_1"><i><font color="Green" title="E56">A51</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>
;<br/><i><font color="Green" title="E59">A54</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5_1_1"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5_1_1"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="txt" href="ami_4.html#E12:17_4_5_1_1"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>
;<br/><a NAME="E17:17_4_5_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</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>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</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>  )
 ;<br/><a NAME="E18:17_4_5_1_1"/><b>then </b><i><font color="Green" title="E60">A55</font></i>: 
( (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4 ) or (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E4:17_4_5_1_1"><i><font color="Green" title="E47">A42</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="txt" href="ami_4.html#E16:17_4_5_1_1"><i><font color="Green" title="E59">A54</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>;<br/><i><font color="Green" title="E61">A56</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E4:17_4_5_1_1"><i><font color="Green" title="E47">A42</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E4:17_4_5_1_1"><i><font color="Green" title="E47">A42</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="txt" href="ami_4.html#E15:17_4_5_1_1"><i><font color="Green" title="E58">A53</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>
;<br/><i><font color="Green" title="E62">A57</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E4:17_4_5_1_1"><i><font color="Green" title="E47">A42</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E4:17_4_5_1_1"><i><font color="Green" title="E47">A42</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="txt" href="ami_4.html#E16:17_4_5_1_1"><i><font color="Green" title="E59">A54</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>
;<br/><b>thus </b><a NAME="E21:17_4_5_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E5:17_4_5"><i><font color="Green" title="E43">A38</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4_5_1_1"><i><font color="Green" title="E49">A44</font></i></a>, <a class="txt" href="ami_4.html#E10:17_4_5_1_1"><i><font color="Green" title="E53">A48</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4_5_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="txt" href="ami_4.html#E18:17_4_5_1_1"><i><font color="Green" title="E60">A55</font></i></a></i>;<br/><b>thus </b><a NAME="E22:17_4_5_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E5:17_4_5"><i><font color="Green" title="E43">A38</font></i></a>, <a class="txt" href="ami_4.html#E7:17_4_5_1_1"><i><font color="Green" title="E50">A45</font></i></a>, <a class="txt" href="ami_4.html#E11:17_4_5_1_1"><i><font color="Green" title="E54">A49</font></i></a>, <a class="txt" href="ami_4.html#E15:17_4_5_1_1"><i><font color="Green" title="E58">A53</font></i></a>, <a class="txt" href="ami_4.html#E19:17_4_5_1_1"><i><font color="Green" title="E61">A56</font></i></a></i>;<br/><b>thus </b><a NAME="E23:17_4_5_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E5:17_4_5"><i><font color="Green" title="E43">A38</font></i></a>, <a class="txt" href="ami_4.html#E8:17_4_5_1_1"><i><font color="Green" title="E51">A46</font></i></a>, <a class="txt" href="ami_4.html#E12:17_4_5_1_1"><i><font color="Green" title="E55">A50</font></i></a>, <a class="txt" href="ami_4.html#E16:17_4_5_1_1"><i><font color="Green" title="E59">A54</font></i></a>, <a class="txt" href="ami_4.html#E20:17_4_5_1_1"><i><font color="Green" title="E62">A57</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_4_5_1_2"><b>suppose </b></a><a NAME="E1:17_4_5_1_2"/><i><font color="Green" title="E44">A58</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4
 ;<br/><div class="add"><a NAME="E2:17_4_5_1_2"/><i><font color="Green" title="E45">A59</font></i>: 
<span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font>
 <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="E3:17_4_5_1_2"/>
( <font color="Maroon" title="c19">s1</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c20">s2</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E4:17_4"><i><font color="Green" title="E30">A24</font></i></a>, <a class="txt" href="ami_4.html#E6:17_4"><i><font color="Green" title="E32">A26</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5"><i><font color="Green" title="E40">A35</font></i></a>, <a class="txt" href="ami_4.html#E1:17_4_5_1_2"><i><font color="Green" title="E44">A58</font></i></a>, <a class="txt" href="ami_4.html#E7"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><a NAME="E4:17_4_5_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E2:17_4_5_1_2"><i><font color="Green" title="E45">A59</font></i></a>, <a class="ref" href="ami_1.html#T89" title="AMI_1:th.89">AMI_1:89</a></i>;<br/><b>hence </b><a NAME="E5:17_4_5_1_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c26">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">j</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E1:17_4_5"><i><font color="Green" title="E40">A35</font></i></a>, <a class="txt" href="ami_4.html#E2:17_4_5"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="ami_4.html#E3:17_4_5"><i><font color="Green" title="E42">A37</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E15:17_4"/><i><font color="Green" title="E40">A60</font></i>: 
4 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E16:17_4"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c23">k</font>]
 
<b>from </b><i><a class="ref" href="nat_d.html#S2" title="NAT_D:sch.2">NAT_D:sch 2</a>(<a class="txt" href="ami_4.html#E13:17_4"><i><font color="Green" title="E38">A32</font></i></a>, <a class="txt" href="ami_4.html#E15:17_4"><i><font color="Green" title="E40">A60</font></i></a>, <a class="txt" href="ami_4.html#E14:17_4"><i><font color="Green" title="E39">A34</font></i></a>);<br/></i>
<a NAME="E17:17_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E12:17_4"><i><font color="Green" title="E37">A31</font></i></a>, <a class="ref" href="grfunc_1.html#T92" title="GRFUNC_1:th.92">GRFUNC_1:92</a></i>;<br/>
<b>hence </b><a NAME="E18:17_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">s1</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p5">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c20">s2</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p5">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E8:17_4"><i><font color="Green" title="E34">A28</font></i></a>, <a class="txt" href="ami_4.html#E11:17_4"><i><font color="Green" title="E36">A30</font></i></a>, <a class="ref" href="relat_1.html#T185" title="RELAT_1:th.185">RELAT_1:185</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:17"/><i><font color="Green" title="E27">A61</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">t</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a><br/>

<b>assume </b><a NAME="E1:17_5"/><i><font color="Green" title="E28">A62</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 ;<br/>

<a NAME="E2:17_5"/><b>then </b><i><font color="Green" title="E29">A63</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E13:17"><i><font color="Green" title="E23">A11</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E3:17_5"/><i><font color="Green" title="E30">A64</font></i>: 
<font color="Maroon" title="c19">t</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="ami_4.html#E14:17"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="ami_4.html#E1:17_5"><i><font color="Green" title="E28">A62</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E4:17_5"/><i><font color="Green" title="E31">A65</font></i>: 
( <font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> &amp; <font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E16:17"><i><font color="Green" title="E25">A17</font></i></a>, <a class="txt" href="ami_4.html#E1:17_5"><i><font color="Green" title="E28">A62</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c20">i1'</font> = <font color="Maroon" title="c14">i1</font>, <font color="Maroon" title="c21">i2'</font> = <font color="Maroon" title="c15">i2</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="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/>
<b>set </b><font color="Maroon" title="c22">t'</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_5_1"/>
( <font color="Maroon" title="c14">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c15">i2</font> or <font color="Maroon" title="c14">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> or <font color="Maroon" title="c14">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c15">i2</font> )
 </span><b>by </b><i><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="17_5_1_1"><b>suppose </b></a><a NAME="E1:17_5_1_1"/>
<font color="Maroon" title="c14">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c15">i2</font>
 ;<br/><div class="add"><a NAME="E2:17_5_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c19">t</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Olive" title="b1">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5"><i><font color="Green" title="E30">A64</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5"><i><font color="Green" title="E31">A65</font></i></a>, <a class="txt" href="ami_4.html#E15"><i><font color="Green" title="E11">Lm5</font></i></a></i>;<br/><b>hence </b><a NAME="E3:17_5_1_1"/>
<font color="Maroon" title="c19">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#T83" title="AMI_1:th.83">AMI_1:83</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1_2"><b>suppose </b></a><a NAME="E1:17_5_1_2"/><i><font color="Green" title="E32">A66</font></i>: 
<font color="Maroon" title="c14">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font>
 ;<br/><div class="add"><i><font color="Green" title="E33">A67</font></i>: <font color="Maroon" title="c14">i1</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c15">i2</font> = 
<font color="Maroon" title="c20">i1'</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c21">i2'</font>

<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="ami_4.html#E1:17_5_1_2"><i><font color="Green" title="E32">A66</font></i></a>, <a class="ref" href="nat_d.html#T25" title="NAT_D:th.25">NAT_D:25</a></i>
;<br/><a NAME="E3:17_5_1_2"/><i><font color="Green" title="E34">A68</font></i>: 
( <font color="Maroon" title="c19">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<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></span>)</span> )
 <b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/><a NAME="E4:17_5_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5"><i><font color="Green" title="E30">A64</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5"><i><font color="Green" title="E31">A65</font></i></a>, <a class="txt" href="ami_4.html#E14"><i><font color="Green" title="E10">Lm4</font></i></a></i>;<br/><a NAME="E5:17_5_1_2"/><b>then </b>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 4
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5"><i><font color="Green" title="E30">A64</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5"><i><font color="Green" title="E31">A65</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5_1_2"><i><font color="Green" title="E33">A67</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5_1_2"><i><font color="Green" title="E34">A68</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green" title="E9">Lm3</font></i></a></i>;<br/><a NAME="E6:17_5_1_2"/><b>then </b>
<font color="Maroon" title="c19">t</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E7"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><b>hence </b><a NAME="E7:17_5_1_2"/>
<font color="Maroon" title="c19">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#T83" title="AMI_1:th.83">AMI_1:83</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1_3"><b>suppose </b></a><a NAME="E1:17_5_1_3"/><i><font color="Green" title="E32">A69</font></i>: 
<font color="Maroon" title="c14">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c15">i2</font>
 ;<br/><div class="add"><i><font color="Green" title="E33">A70</font></i>: <font color="Maroon" title="c14">i1</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c15">i2</font> = 
<font color="Maroon" title="c20">i1'</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c21">i2'</font>

<br/>.= 
<font color="Maroon" title="c20">i1'</font>
<b>by </b><i><a class="txt" href="ami_4.html#E1:17_5_1_3"><i><font color="Green" title="E32">A69</font></i></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/><a NAME="E3:17_5_1_3"/><i><font color="Green" title="E34">A71</font></i>: 
( <font color="Maroon" title="c19">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<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></span>)</span> )
 <b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/><a NAME="E4:17_5_1_3"/><b>then </b><i><font color="Green" title="E35">A72</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> )
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5"><i><font color="Green" title="E30">A64</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5"><i><font color="Green" title="E31">A65</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5_1_3"><i><font color="Green" title="E33">A70</font></i></a>, <a class="txt" href="ami_4.html#E14"><i><font color="Green" title="E10">Lm4</font></i></a></i>;<br/><a NAME="E5:17_5_1_3"/><b>then </b>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5"><i><font color="Green" title="E30">A64</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5"><i><font color="Green" title="E31">A65</font></i></a>, <a class="txt" href="ami_4.html#E3:17_5_1_3"><i><font color="Green" title="E34">A71</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green" title="E9">Lm3</font></i></a></i>;<br/><a NAME="E6:17_5_1_3"/><b>then </b><i><font color="Green" title="E36">A73</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4 <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D41" title="AMI_1:def.41">AMI_1:def 41</a></i>;<br/><a NAME="E7:17_5_1_3"/>
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4
 <b>by </b><i><a class="txt" href="ami_4.html#E2:17_5"><i><font color="Green" title="E29">A63</font></i></a>, <a class="ref" href="ami_1.html#T86" title="AMI_1:th.86">AMI_1:86</a></i>;<br/><b>then consider </b><font color="Maroon" title="c23">k0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E9:17_5_1_3"/><i><font color="Green" title="E37">A74</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4 <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k0</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E1:17_5_1_3"><i><font color="Green" title="E32">A69</font></i></a>, <a class="txt" href="ami_4.html#E4:17_5_1_3"><i><font color="Green" title="E35">A72</font></i></a>, <a class="txt" href="ami_4.html#E6:17_5_1_3"><i><font color="Green" title="E36">A73</font></i></a>, <a class="txt" href="ami_4.html#E15"><i><font color="Green" title="E11">Lm5</font></i></a></i>;<br/><a NAME="E10:17_5_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">k0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c23">k0</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/><a NAME="E11:17_5_1_3"/><b>then </b>
<font color="Maroon" title="c19">t</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">k0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E9:17_5_1_3"><i><font color="Green" title="E37">A74</font></i></a>, <a class="ref" href="ami_1.html#T91" title="AMI_1:th.91">AMI_1:91</a></i>;<br/><b>hence </b><a NAME="E12:17_5_1_3"/>
<font color="Maroon" title="c19">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#T83" title="AMI_1:th.83">AMI_1:83</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E19:17"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> is   <a href="ami_1.html#NM6" title="AMI_1:NM.6">pre-program</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="txt" href="ami_4.html#E17:17"><i><font color="Green" title="E26">A20</font></i></a></i>;<br/>

<a NAME="E20:17"/><i><font color="Green" title="E28">A75</font></i>: 
<a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c15">i2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="ami_4.html#T12" target="_self" title="AMI_4:th.12">Th12</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c19">t</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E22:17"/><i><font color="Green" title="E29">A76</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T82" title="AMI_1:th.82">AMI_1:82</a></i>;<br/>
<a NAME="E23:17"/><i><font color="Green" title="E30">A77</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<a NAME="E24:17"/><b>then </b><i><font color="Green" title="E31">A78</font></i>: 
(  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E25:17"/><i><font color="Green" title="E32">A79</font></i>: 
<font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E26:17"/><b>then </b><i><font color="Green" title="E33">A80</font></i>: 
<font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E22:17"><i><font color="Green" title="E29">A76</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E27:17"/>
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E28:17"/><b>then </b>
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E11:17"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E29:17"/><b>then </b><i><font color="Green" title="E34">A81</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E22:17"><i><font color="Green" title="E29">A76</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E30:17"/><i><font color="Green" title="E35">A82</font></i>: 
<font color="Maroon" title="c19">t</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="ami_4.html#E14:17"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="ami_4.html#E22:17"><i><font color="Green" title="E29">A76</font></i></a>, <a class="ref" href="ami_1.html#T92" title="AMI_1:th.92">AMI_1:92</a></i>;<br/>
<a NAME="E31:17"/>
 <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
;<br/>
<a NAME="E32:17"/><b>then </b><i><font color="Green" title="E36">A83</font></i>: 
 <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c19">t</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E33:17"/>
( <font color="Maroon" title="c16">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> &amp; <font color="Maroon" title="c16">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E4:17"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="ami_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>;<br/>
<a NAME="E34:17"/><b>then </b>
( <font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> &amp; <font color="Maroon" title="c19">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">i2</font> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E24:17"><i><font color="Green" title="E31">A78</font></i></a>, <a class="txt" href="ami_4.html#E26:17"><i><font color="Green" title="E33">A80</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E35:17"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c15">i2</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E3:17"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="ami_4.html#E29:17"><i><font color="Green" title="E34">A81</font></i></a>, <a class="txt" href="ami_4.html#E30:17"><i><font color="Green" title="E35">A82</font></i></a>, <a class="ref" href="ami_4.html#T10" target="_self" title="AMI_4:th.10">Th10</a></i>;<br/>
<a NAME="E36:17"/><b>then </b><i><font color="Green" title="E37">A84</font></i>: 
<a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c19">t</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E20:17"><i><font color="Green" title="E28">A75</font></i></a>, <a class="txt" href="ami_4.html#E32:17"><i><font color="Green" title="E36">A83</font></i></a>, <a class="ref" href="funct_4.html#T90" title="FUNCT_4:th.90">FUNCT_4:90</a></i>;<br/>
<a NAME="E37:17"/><i><font color="Green" title="E38">A85</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E25:17"><i><font color="Green" title="E32">A79</font></i></a>, <a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/>
<a NAME="E38:17"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c15">i2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E39:17"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c15">i2</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c16">s</font>
 
<b>by </b><i><a class="txt" href="ami_4.html#E23:17"><i><font color="Green" title="E30">A77</font></i></a>, <a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/>
<a NAME="E40:17"/><b>then </b><i><font color="Green" title="E39">A86</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c15">i2</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E37:17"><i><font color="Green" title="E38">A85</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E41:17"/>
 <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c19">t</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p5">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E17:17"><i><font color="Green" title="E26">A20</font></i></a>, <a class="txt" href="ami_4.html#E18:17"><i><font color="Green" title="E27">A61</font></i></a>, <a class="txt" href="ami_4.html#E22:17"><i><font color="Green" title="E29">A76</font></i></a>, <a class="ref" href="ami_1.html#D28" title="AMI_1:def.28">AMI_1:def 28</a></i>;<br/>
<b>hence </b><a NAME="E42:17"/>
<a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K17" title="AMI_1:func.17">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c16">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E20:17"><i><font color="Green" title="E28">A75</font></i></a>, <a class="txt" href="ami_4.html#E36:17"><i><font color="Green" title="E37">A84</font></i></a>, <a class="txt" href="ami_4.html#E40:17"><i><font color="Green" title="E39">A86</font></i></a>, <a class="ref" href="relat_1.html#T186" title="RELAT_1:th.186">RELAT_1:186</a></i>;<br/>


</div>
