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

<span class="kw">set </span><font color="Maroon" title="c13">q</font> =  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">p</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>);<br/>
<span class="kw">let </span><font color="Maroon" title="c15">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D14" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a> or  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  &amp; <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="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) ) )</span><br/>

<a NAME="E1:18"/>
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</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>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T20" title="MEMSTR_0:th.20">MEMSTR_0:20</a></span>;<br/>
<a NAME="E2:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<span class="kw">assume </span><a NAME="E3:18"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Function</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  &amp; <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="Olive">b<sub>1</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive">b<sub>1</sub></font></span>)</span>) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">i1</font>, <font color="Maroon" title="c17">i2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E5:18"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c16">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> 
 <span class="kw">and </span><br/><a NAME="E6:18"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c17">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> 
 <span class="kw">and </span><br/><a NAME="E7:18"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>) <a href="ami_3.html#K13" title="AMI_3:func.13">--&gt;</a> (<font color="Maroon" title="c16">i1</font>,<font color="Maroon" title="c17">i2</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th11</a></span>;<br/>
<a NAME="E8:18"/>
<font color="Maroon" title="c15">x</font> <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_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <font color="Maroon" title="c16">i1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <font color="Maroon" title="c17">i2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">d</font> = <font color="Maroon" title="c15">x</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c19">t</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a><span class="kw"> such that </span><br/><a NAME="E11:18"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T141" title="PBOOLE:th.141">PBOOLE:141</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c20">T</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a><span class="kw"> such that </span><br/><a NAME="E13:18"/><span class="lab"><font color="Green" title="E22">C10</font></span>: 
 <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">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T145" title="PBOOLE:th.145">PBOOLE:145</a></span>;<br/>
<a NAME="E14:18"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</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#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>;<br/>
<a NAME="E15:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A12</font></span>: 
 <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E16:18"/><span class="lab"><font color="Green" title="E25">A21</font></span>: 
 <a href="ami_3.html#K11" title="AMI_3:func.11">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E17:18"/><span class="lab"><font color="Green" title="E26">A22</font></span>: 
 for <font color="Olive" title="b1">t</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  st <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</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#K11" title="AMI_3:func.11">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="c16">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">t</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c21">t</font> implies ( <font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">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="c16">i1</font> &amp; <font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:18_1"/><span class="lab"><font color="Green" title="E27">Z</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c21">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">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="c16">i1</font> &amp; <font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font> )</span><br/>

<a NAME="E2:18_1"/>
<font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E3:18_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A24</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c21">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1"><span class="lab"><font color="Green" title="E27">Z</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<font color="Maroon" title="c18">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E25">A21</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c16">i1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c21">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<font color="Maroon" title="c18">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E3:18_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c17">i2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E18:18"/><span class="lab"><font color="Green" title="E27">A25</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</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"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E28">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:18_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c21">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:18_2"/><span class="lab"><font color="Green" title="E29">A27</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:18_2"/><span class="lab"><font color="Green" title="E30">A28</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/><a NAME="E5:18_2"/><span class="lab"><font color="Green" title="E31">A29</font></span>: 
( <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:18"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="txt" href="#E3:18_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:18_2"/>
( <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E4:18_2"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:18_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_2"><span class="lab"><font color="Green" title="E31">A29</font></span></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a>, <a class="ref" href="ami_3.html#T13" title="AMI_3:th.13">AMI_3:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E20:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A30</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T32" title="FUNCT_4:th.32">FUNCT_4:32</a></span>;<br/>
<a NAME="E21:18"/><span class="lab"><font color="Green" title="E30">A31</font></span>: 
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:18"><span class="lab"><font color="Green" title="E27">A25</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E22:18"/>
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:18"><span class="lab"><font color="Green" title="E28">A26</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E23:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A32</font></span>: 
 not  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E30">A31</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">set </span><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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">C</font> = 5;<br/>
<span class="lab"><font color="Green" title="E32">A33</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</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">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p4">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E30">A31</font></span></a>, <a class="ref" href="memstr_0.html#T24" title="MEMSTR_0:th.24">MEMSTR_0:24</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</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="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>
<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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T2" title="ENUMSET1:th.2">ENUMSET1:2</a></span>
;<br/>
<a NAME="E25:18"/><span class="lab"><font color="Green" title="E33">A34</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:18"><span class="lab"><font color="Green" title="E29">A30</font></span></a>, <a class="ref" href="relat_1.html#T11" title="RELAT_1:th.11">RELAT_1:11</a></span>;<br/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E31">A32</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
;<br/>
<a NAME="E27:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A35</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:18"><span class="lab"><font color="Green" title="E33">A34</font></span></a>, <a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E30">A31</font></span></a>, <a class="ref" href="memstr_0.html#D8" title="MEMSTR_0:def.8">MEMSTR_0:def 8</a></span>;<br/>
<a NAME="E28:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A36</font></span>: 
<font color="Maroon" title="c19">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="memstr_0.html#T17" title="MEMSTR_0:th.17">MEMSTR_0:17</a></span>;<br/>
<a NAME="E29:18"/><span class="lab"><font color="Green" title="E36">A38</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c23">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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c24">C</font> = 5;<br/>
<span class="kw">let </span><font color="Maroon" title="c25">P</font>, <font color="Maroon" title="c26">Q</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D10" title="EXTPRO_1:def.10">EXTPRO_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <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="c25">P</font> or  not  <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="c26">Q</font> or  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>2</sub></font> or  for <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18_5"/><span class="lab"><font color="Green" title="E37">A39</font></span>: 
 <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="c25">P</font>
 <span class="kw">and </span><br/><a NAME="E2:18_5"/><span class="lab"><font color="Green" title="E38">A40</font></span>: 
 <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="c26">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>2</sub></font> or  for <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c27">s1</font>, <font color="Maroon" title="c28">s2</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c27">s1</font> or  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c28">s2</font> or  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<font color="Olive">b<sub>1</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<font color="Olive">b<sub>1</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:18_5"/><span class="lab"><font color="Green" title="E39">A41</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c27">s1</font>
 <span class="kw">and </span><br/><a NAME="E4:18_5"/><span class="lab"><font color="Green" title="E40">A42</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c28">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<font color="Olive">b<sub>1</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<font color="Olive">b<sub>1</sub></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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span></span><br/>

<a NAME="E5:18_5"/><span class="lab"><font color="Green" title="E41">A43</font></span>: 
( <font color="Maroon" title="c28">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#K11" title="AMI_3:func.11">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="c16">i1</font> &amp; <font color="Maroon" title="c28">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E40">A42</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c29">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<font color="Maroon" title="c29">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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<font color="Maroon" title="c29">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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span></span><br/>

<span class="kw">defpred </span><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> ] <span class="kw">means </span>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,$1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,$1)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,$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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,$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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,$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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,$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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> );<br/>
<a NAME="E6:18_5"/><span class="lab"><font color="Green" title="E42">A45</font></span>: 
(  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c27">s1</font> &amp;  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c28">s2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/>
<a NAME="E7:18_5"/><span class="lab"><font color="Green" title="E43">A46</font></span>: 
<font color="Maroon" title="c27">s1</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:18"><span class="lab"><font color="Green" title="E34">A35</font></span></a>, <a class="txt" href="#E3:18_5"><span class="lab"><font color="Green" title="E39">A41</font></span></a>, <a class="ref" href="memstr_0.html#T17" title="MEMSTR_0:th.17">MEMSTR_0:17</a></span>;<br/>
<span class="lab"><font color="Green" title="E44">A47</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<font color="Maroon" title="c29">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<font color="Maroon" title="c29">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
;<br/>
<a NAME="E9:18_5"/><span class="lab"><font color="Green" title="E45">A49</font></span>: 
<font color="Maroon" title="c28">s2</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:18"><span class="lab"><font color="Green" title="E34">A35</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E40">A42</font></span></a>, <a class="ref" href="memstr_0.html#T17" title="MEMSTR_0:th.17">MEMSTR_0:17</a></span>;<br/>
<a NAME="E10:18_5"/><span class="lab"><font color="Green" title="E46">A50</font></span>: 
 for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">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="18_5_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c30">i</font>, <font color="Maroon" title="c31">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>2</sub></font>[4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font>] &amp; <font color="Maroon" title="c31">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="c31">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 implies <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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>] )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18_5_2"/><span class="lab"><font color="Green" title="E47">A51</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:18_5_2"/><span class="lab"><font color="Green" title="E48">A52</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:18_5_2"/><span class="lab"><font color="Green" title="E49">A53</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c31">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>  or  not <font color="Maroon" title="c31">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 or <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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>] )</span><br/>

<a NAME="E4:18_5_2"/><span class="lab"><font color="Green" title="E50">A54</font></span>: 
<font color="Maroon" title="c30">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:18_5_2"/>
( <font color="Maroon" title="c31">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="c31">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>]</span><br/>

<a NAME="E6:18_5_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A55</font></span>: 
( <font color="Maroon" title="c31">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c31">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c31">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c31">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T28" title="NAT_1:th.28">NAT_1:28</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_5_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_5_2_1"/>
(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E9:18_5"><span class="lab"><font color="Green" title="E45">A49</font></span></a>, <a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E5:18_5"><span class="lab"><font color="Green" title="E41">A43</font></span></a>, <a class="txt" href="#E4:18_5_2"><span class="lab"><font color="Green" title="E50">A54</font></span></a>, <a class="txt" href="ami_4.html#E11"><span class="lab"><font color="Green" title="E10">Lm4</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_5_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_5_2_1_1"/><span class="lab"><font color="Green" title="E52">A56</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>]</span><br/><div class="add"><span class="lab"><font color="Green" title="E53">A58</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E2:18_5_2"><span class="lab"><font color="Green" title="E48">A52</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
;<br/><span class="lab"><font color="Green" title="E54">A59</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E3:18_5_2"><span class="lab"><font color="Green" title="E49">A53</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
;<br/><span class="lab"><font color="Green" title="E55">A60</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E3:18_5_2"><span class="lab"><font color="Green" title="E49">A53</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>
;<br/><a NAME="E5:18_5_2_1_1"/><span class="lab"><font color="Green" title="E56">A61</font></span>: 
<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="c30">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="c30">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="E6:18_5_2_1_1"/><span class="lab"><font color="Green" title="E57">A62</font></span>: 
<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="c30">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="c30">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="E7:18_5_2_1_1"/><span class="lab"><font color="Green" title="E58">A63</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>;<br/><a NAME="E8:18_5_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A64</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>;<br/><a NAME="E9:18_5_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A65</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>;<br/><a NAME="E10:18_5_2_1_1"/><span class="lab"><font color="Green" title="E61">A66</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A67</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E7:18_5_2_1_1"><span class="lab"><font color="Green" title="E58">A63</font></span></a>, <a class="txt" href="#E3:18_5_2_1_1"><span class="lab"><font color="Green" title="E54">A59</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
;<br/><span class="lab"><font color="Green" title="E63">A68</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E10:18_5_2_1_1"><span class="lab"><font color="Green" title="E61">A66</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E7:18_5_2_1_1"><span class="lab"><font color="Green" title="E58">A63</font></span></a>, <a class="txt" href="#E2:18_5_2_1_1"><span class="lab"><font color="Green" title="E53">A58</font></span></a>, <a class="txt" href="#E4:18_5_2_1_1"><span class="lab"><font color="Green" title="E55">A60</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
;<br/><a NAME="E13:18_5_2_1_1"/><span class="lab"><font color="Green" title="E64">A69</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E10:18_5_2_1_1"><span class="lab"><font color="Green" title="E61">A66</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>;<br/><a NAME="E14:18_5_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A70</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>;<br/><span class="lab"><font color="Green" title="E66">A71</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E10:18_5_2_1_1"><span class="lab"><font color="Green" title="E61">A66</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="txt" href="#E7:18_5_2_1_1"><span class="lab"><font color="Green" title="E58">A63</font></span></a>, <a class="txt" href="#E2:18_5_2_1_1"><span class="lab"><font color="Green" title="E53">A58</font></span></a>, <a class="txt" href="#E4:18_5_2_1_1"><span class="lab"><font color="Green" title="E55">A60</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a></span>
;<br/><a NAME="E16:18_5_2_1_1"/><span class="lab"><font color="Green" title="E67">A72</font></span>: 
<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="c30">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="c30">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/><span class="lab"><font color="Green" title="E68">A73</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="txt" href="#E13:18_5_2_1_1"><span class="lab"><font color="Green" title="E64">A69</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="txt" href="#E8:18_5_2_1_1"><span class="lab"><font color="Green" title="E59">A64</font></span></a>, <a class="txt" href="#E11:18_5_2_1_1"><span class="lab"><font color="Green" title="E62">A67</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>
;<br/><span class="lab"><font color="Green" title="E69">A74</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="txt" href="#E13:18_5_2_1_1"><span class="lab"><font color="Green" title="E64">A69</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="txt" href="#E8:18_5_2_1_1"><span class="lab"><font color="Green" title="E59">A64</font></span></a>, <a class="txt" href="#E12:18_5_2_1_1"><span class="lab"><font color="Green" title="E63">A68</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>
;<br/><a NAME="E19:18_5_2_1_1"/>
( <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">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="E20:18_5_2_1_1"/><span class="kw">then </span>
( (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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> 4 &amp;  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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> 4 ) or (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E16:18_5_2_1_1"><span class="lab"><font color="Green" title="E67">A72</font></span></a>, <a class="txt" href="#E14:18_5_2_1_1"><span class="lab"><font color="Green" title="E65">A70</font></span></a>, <a class="txt" href="#E9:18_5_2_1_1"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E18:18_5_2_1_1"><span class="lab"><font color="Green" title="E69">A74</font></span></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th8</a></span>;<br/><span class="kw">hence </span><a NAME="E21:18_5_2_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18_5_2"><span class="lab"><font color="Green" title="E51">A55</font></span></a>, <a class="txt" href="#E10:18_5_2_1_1"><span class="lab"><font color="Green" title="E61">A66</font></span></a>, <a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E1:18_5_2_1_1"><span class="lab"><font color="Green" title="E52">A56</font></span></a>, <a class="ref" href="ami_4.html#T2" target="_self" title="AMI_4:th.2">Th5</a>, <a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E5:18_5_2_1_1"><span class="lab"><font color="Green" title="E56">A61</font></span></a>, <a class="ref" href="ami_4.html#T3" target="_self" title="AMI_4:th.3">Th6</a>, <a class="txt" href="#E8:18_5_2_1_1"><span class="lab"><font color="Green" title="E59">A64</font></span></a>, <a class="txt" href="#E14:18_5_2_1_1"><span class="lab"><font color="Green" title="E65">A70</font></span></a>, <a class="txt" href="#E6:18_5_2_1_1"><span class="lab"><font color="Green" title="E57">A62</font></span></a>, <a class="ref" href="ami_4.html#T4" target="_self" title="AMI_4:th.4">Th7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> )</span><br/><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E16:18_5_2_1_1"><span class="lab"><font color="Green" title="E67">A72</font></span></a>, <a class="txt" href="#E14:18_5_2_1_1"><span class="lab"><font color="Green" title="E65">A70</font></span></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E16:18_5_2_1_1"><span class="lab"><font color="Green" title="E67">A72</font></span></a>, <a class="txt" href="#E9:18_5_2_1_1"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E17:18_5_2_1_1"><span class="lab"><font color="Green" title="E68">A73</font></span></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th8</a></span>
;<br/><span class="kw">hence </span><a NAME="E23:18_5_2_1_1"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">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"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18_5_2"><span class="lab"><font color="Green" title="E51">A55</font></span></a>, <a class="txt" href="#E2:18_5_2_1_1"><span class="lab"><font color="Green" title="E53">A58</font></span></a>, <a class="txt" href="#E15:18_5_2_1_1"><span class="lab"><font color="Green" title="E66">A71</font></span></a>, <a class="txt" href="#E17:18_5_2_1_1"><span class="lab"><font color="Green" title="E68">A73</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><br/><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E16:18_5_2_1_1"><span class="lab"><font color="Green" title="E67">A72</font></span></a>, <a class="txt" href="#E14:18_5_2_1_1"><span class="lab"><font color="Green" title="E65">A70</font></span></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E16:18_5_2_1_1"><span class="lab"><font color="Green" title="E67">A72</font></span></a>, <a class="txt" href="#E9:18_5_2_1_1"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E18:18_5_2_1_1"><span class="lab"><font color="Green" title="E69">A74</font></span></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th8</a></span>
;<br/><span class="kw">hence </span><a NAME="E25:18_5_2_1_1"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18_5_2"><span class="lab"><font color="Green" title="E51">A55</font></span></a>, <a class="txt" href="#E4:18_5_2_1_1"><span class="lab"><font color="Green" title="E55">A60</font></span></a>, <a class="txt" href="#E12:18_5_2_1_1"><span class="lab"><font color="Green" title="E63">A68</font></span></a>, <a class="txt" href="#E18:18_5_2_1_1"><span class="lab"><font color="Green" title="E69">A74</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_5_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_5_2_1_2"/><span class="lab"><font color="Green" title="E52">A75</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>]</span><br/><div class="add"><a NAME="E2:18_5_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">P</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E37">A39</font></span></a>, <a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="ami_4.html#E5"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a></span>;<br/><a NAME="E3:18_5_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A76</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font></span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T20" title="EXTPRO_1:th.20">EXTPRO_1:20</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E4:18_5_2_1_2"/>
<font color="Maroon" title="c26">Q</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<span class="p2">(<span class="default">4 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c30">i</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E38">A40</font></span></a>, <a class="txt" href="#E1:18_5_2_1_2"><span class="lab"><font color="Green" title="E52">A75</font></span></a>, <a class="txt" href="ami_4.html#E5"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:18_5_2_1_2"/>
<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="Maroon" title="c30">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_5_2"><span class="lab"><font color="Green" title="E47">A51</font></span></a>, <a class="txt" href="#E2:18_5_2"><span class="lab"><font color="Green" title="E48">A52</font></span></a>, <a class="txt" href="#E3:18_5_2"><span class="lab"><font color="Green" title="E49">A53</font></span></a>, <a class="txt" href="#E3:18_5_2_1_2"><span class="lab"><font color="Green" title="E53">A76</font></span></a>, <a class="ref" href="extpro_1.html#T20" title="EXTPRO_1:th.20">EXTPRO_1:20</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c27">s1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18_5"><span class="lab"><font color="Green" title="E43">A46</font></span></a>, <a class="ref" href="memstr_0.html#D8" title="MEMSTR_0:def.8">MEMSTR_0:def 8</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c28">s2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18_5"><span class="lab"><font color="Green" title="E45">A49</font></span></a>, <a class="ref" href="memstr_0.html#D8" title="MEMSTR_0:def.8">MEMSTR_0:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<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="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
;<br/>
<a NAME="E12:18_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A77</font></span>: 
<font color="Maroon">S<sub>2</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="txt" href="#E3:18_5"><span class="lab"><font color="Green" title="E39">A41</font></span></a>, <a class="txt" href="#E5:18_5"><span class="lab"><font color="Green" title="E41">A43</font></span></a>, <a class="txt" href="#E6:18_5"><span class="lab"><font color="Green" title="E42">A45</font></span></a></span>;<br/>
<a NAME="E13:18_5"/><span class="lab"><font color="Green" title="E48">A78</font></span>: 
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="E14:18_5"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c29">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_d.html#S2" title="NAT_D:sch.2">NAT_D:sch 2</a>(<a class="txt" href="#E12:18_5"><span class="lab"><font color="Green" title="E47">A77</font></span></a>, <a class="txt" href="#E13:18_5"><span class="lab"><font color="Green" title="E48">A78</font></span></a>, <a class="txt" href="#E10:18_5"><span class="lab"><font color="Green" title="E46">A50</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E15:18_5"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c25">P</font>,<font color="Maroon" title="c27">s1</font>,<font color="Maroon" title="c29">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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">Q</font>,<font color="Maroon" title="c28">s2</font>,<font color="Maroon" title="c29">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">proj1</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:18"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="txt" href="#E8:18_5"><span class="lab"><font color="Green" title="E44">A47</font></span></a>, <a class="ref" href="grfunc_1.html#T31" title="GRFUNC_1:th.31">GRFUNC_1:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">take </span>
<font color="Maroon" title="c18">d</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">d</font> &amp; <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  &amp; <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="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E30:18"/>
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  &amp; <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="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>) )</span><br/>

<a NAME="E31:18"/><span class="lab"><font color="Green" title="E37">A79</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="extpro_1.html#V5" title="EXTPRO_1:attr.5">-halted</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c23">i19</font> = <font color="Maroon" title="c16">i1</font>, <font color="Maroon" title="c24">i29</font> = <font color="Maroon" title="c17">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c25">t</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D11" title="EXTPRO_1:def.11">EXTPRO_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">t</font> or  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not  <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="Olive">b<sub>1</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:18_6"/><span class="lab"><font color="Green" title="E38">B80</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not  <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="Olive">b<sub>1</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c26">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <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="c26">P</font> or <font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:18_6"/><span class="lab"><font color="Green" title="E39">A81</font></span>: 
 <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="c26">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c27">t9</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4);<br/>
<a NAME="E4:18_6"/><span class="lab"><font color="Green" title="E40">A84</font></span>: 
<font color="Maroon" title="c25">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="txt" href="#E2:18_6"><span class="lab"><font color="Green" title="E38">B80</font></span></a></span>;<br/>
<a NAME="E5:18_6"/><span class="lab"><font color="Green" title="E41">A85</font></span>: 
( <font color="Maroon" title="c25">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  &amp; <font color="Maroon" title="c25">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#K11" title="AMI_3:func.11">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="c16">i1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:18"><span class="lab"><font color="Green" title="E34">A35</font></span></a>, <a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="txt" href="#E2:18_6"><span class="lab"><font color="Green" title="E38">B80</font></span></a>, <a class="ref" href="memstr_0.html#T17" title="MEMSTR_0:th.17">MEMSTR_0:17</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_6_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_6_1"/>
( <font color="Maroon" title="c16">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c17">i2</font> or <font color="Maroon" title="c16">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font> or <font color="Maroon" title="c16">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">i2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_6_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_6_1_1"/>
<font color="Maroon" title="c16">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c17">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font></span><br/><div class="add"><a NAME="E2:18_6_1_1"/><span class="kw">then </span>
 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="c26">P</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<font color="Olive" title="b1">k</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="ami_4.html#E13"><span class="lab"><font color="Green" title="E12">Lm6</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_6_1_1"/>
<font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T16" title="EXTPRO_1:th.16">EXTPRO_1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_6_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_6_1_2"/><span class="lab"><font color="Green" title="E42">A86</font></span>: 
<font color="Maroon" title="c16">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font></span><br/><div class="add"><span class="lab"><font color="Green" title="E43">A87</font></span>: <font color="Maroon" title="c16">i1</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c17">i2</font> = 
<font color="Maroon" title="c23">i19</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c24">i29</font>

<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_6_1_2"><span class="lab"><font color="Green" title="E42">A86</font></span></a>, <a class="ref" href="nat_d.html#T25" title="NAT_D:th.25">NAT_D:25</a></span>
;<br/><a NAME="E3:18_6_1_2"/><span class="lab"><font color="Green" title="E44">A88</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<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>)
 ;<br/><a NAME="E4:18_6_1_2"/>
<font color="Maroon" title="c25">t</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/><a NAME="E5:18_6_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,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#K11" title="AMI_3:func.11">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="c25">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#K11" title="AMI_3:func.11">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="c25">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="#E3:18_6_1_2"><span class="lab"><font color="Green" title="E44">A88</font></span></a>, <a class="txt" href="ami_4.html#E12"><span class="lab"><font color="Green" title="E11">Lm5</font></span></a></span>;<br/><a NAME="E6:18_6_1_2"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="#E2:18_6_1_2"><span class="lab"><font color="Green" title="E43">A87</font></span></a>, <a class="txt" href="#E3:18_6_1_2"><span class="lab"><font color="Green" title="E44">A88</font></span></a>, <a class="txt" href="ami_4.html#E11"><span class="lab"><font color="Green" title="E10">Lm4</font></span></a></span>;<br/><a NAME="E7:18_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c26">P</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="ami_4.html#E5"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:18_6_1_2"/>
<font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T16" title="EXTPRO_1:th.16">EXTPRO_1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_6_1_3"><span class="kw">suppose </span></a><a NAME="E1:18_6_1_3"/><span class="lab"><font color="Green" title="E42">A89</font></span>: 
<font color="Maroon" title="c16">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font></span><br/><div class="add"><a NAME="E2:18_6_1_3"/><span class="lab"><font color="Green" title="E43">A90</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<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>)
 ;<br/><a NAME="E3:18_6_1_3"/><span class="lab"><font color="Green" title="E44">A92</font></span>: 
<font color="Maroon" title="c25">t</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/><font color="Maroon" title="c16">i1</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c17">i2</font> = 
<font color="Maroon" title="c23">i19</font> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c24">i29</font>

<br/>.= 
<font color="Maroon" title="c23">i19</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_6_1_3"><span class="lab"><font color="Green" title="E42">A89</font></span></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></span>
;<br/><a NAME="E5:18_6_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A93</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="#E3:18_6_1_3"><span class="lab"><font color="Green" title="E44">A92</font></span></a>, <a class="txt" href="#E2:18_6_1_3"><span class="lab"><font color="Green" title="E43">A90</font></span></a>, <a class="txt" href="ami_4.html#E12"><span class="lab"><font color="Green" title="E11">Lm5</font></span></a></span>;<br/><a NAME="E6:18_6_1_3"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="#E2:18_6_1_3"><span class="lab"><font color="Green" title="E43">A90</font></span></a>, <a class="txt" href="ami_4.html#E11"><span class="lab"><font color="Green" title="E10">Lm4</font></span></a></span>;<br/><a NAME="E7:18_6_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A94</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4) is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D9" title="MEMSTR_0:def.9">MEMSTR_0:def 9</a></span>;<br/><a NAME="E8:18_6_1_3"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,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#K11" title="AMI_3:func.11">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="c17">i2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="#E5:18_6"><span class="lab"><font color="Green" title="E41">A85</font></span></a>, <a class="txt" href="#E4:18_6"><span class="lab"><font color="Green" title="E40">A84</font></span></a>, <a class="txt" href="#E3:18_6_1_3"><span class="lab"><font color="Green" title="E44">A92</font></span></a>, <a class="txt" href="#E2:18_6_1_3"><span class="lab"><font color="Green" title="E43">A90</font></span></a>, <a class="txt" href="ami_4.html#E12"><span class="lab"><font color="Green" title="E11">Lm5</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c28">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> <span class="kw"> such that </span><br/><a NAME="E10:18_6_1_3"/><span class="lab"><font color="Green" title="E47">A95</font></span>: 
<font color="Maroon" title="c26">P</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,4)</span>)</span>,<font color="Maroon" title="c28">k0</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E1:18_6_1_3"><span class="lab"><font color="Green" title="E42">A89</font></span></a>, <a class="txt" href="#E5:18_6_1_3"><span class="lab"><font color="Green" title="E45">A93</font></span></a>, <a class="txt" href="#E7:18_6_1_3"><span class="lab"><font color="Green" title="E46">A94</font></span></a>, <a class="txt" href="#E3:18_6"><span class="lab"><font color="Green" title="E39">A81</font></span></a>, <a class="txt" href="ami_4.html#E13"><span class="lab"><font color="Green" title="E12">Lm6</font></span></a></span>;<br/><a NAME="E11:18_6_1_3"/>
<font color="Maroon" title="c26">P</font> <a href="compos_1.html#R1" title="COMPOS_1:pred.1">halts_at</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c26">P</font>,<font color="Maroon" title="c25">t</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">k0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18_6_1_3"><span class="lab"><font color="Green" title="E47">A95</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E12:18_6_1_3"/>
<font color="Maroon" title="c26">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c25">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T16" title="EXTPRO_1:th.16">EXTPRO_1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E32:18"/>
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of  <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:18"><span class="lab"><font color="Green" title="E36">A38</font></span></a>, <a class="txt" href="#E31:18"><span class="lab"><font color="Green" title="E37">A79</font></span></a>, <a class="ref" href="extpro_1.html#D12" title="EXTPRO_1:def.12">EXTPRO_1:def 12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>)</span><br/>

<a NAME="E33:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A98</font></span>: 
 <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c20">T</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E22">C10</font></span></a>, <a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="extpro_1.html#D13" title="EXTPRO_1:def.13">EXTPRO_1:def 13</a></span>;<br/>
<a NAME="E34:18"/>
 <a href="ami_3.html#K11" title="AMI_3:func.11">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="E35:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A99</font></span>: 
 <a href="ami_3.html#K11" title="AMI_3:func.11">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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c20">T</font>,<font color="Maroon" title="c19">t</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E36:18"/><span class="lab"><font color="Green" title="E40">A101</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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="c16">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>;<br/>
<a NAME="E37:18"/><span class="lab"><font color="Green" title="E41">A102</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>;<br/>
<a NAME="E38:18"/><span class="lab"><font color="Green" title="E42">A103</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<a NAME="E39:18"/><span class="lab"><font color="Green" title="E43">A104</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E42">A103</font></span></a>, <a class="ref" href="relat_1.html#T11" title="RELAT_1:th.11">RELAT_1:11</a></span>;<br/>
<a NAME="E40:18"/><span class="lab"><font color="Green" title="E44">A105</font></span>: 
<font color="Maroon" title="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E42">A103</font></span></a>, <a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E41:18"/><span class="lab"><font color="Green" title="E45">A106</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</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#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>;<br/>
<a NAME="E42:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">BB</font></span>: 
 <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E43:18"/><span class="lab"><font color="Green" title="E47">A107</font></span>: 
<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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:18"><span class="lab"><font color="Green" title="E44">A105</font></span></a>, <a class="txt" href="#E37:18"><span class="lab"><font color="Green" title="E41">A102</font></span></a>, <a class="txt" href="#E42:18"><span class="lab"><font color="Green" title="E46">BB</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<a NAME="E44:18"/><span class="lab"><font color="Green" title="E48">AA</font></span>: 
 <a href="ami_3.html#K11" title="AMI_3:func.11">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:18"><span class="lab"><font color="Green" title="E45">A106</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E45:18"/>
<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#K11" title="AMI_3:func.11">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="c16">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:18"><span class="lab"><font color="Green" title="E44">A105</font></span></a>, <a class="txt" href="#E36:18"><span class="lab"><font color="Green" title="E40">A101</font></span></a>, <a class="txt" href="#E44:18"><span class="lab"><font color="Green" title="E48">AA</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<a NAME="E46:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A109</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c20">T</font>,<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#K11" title="AMI_3:func.11">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="c16">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E28:18"><span class="lab"><font color="Green" title="E35">A36</font></span></a>, <a class="txt" href="#E43:18"><span class="lab"><font color="Green" title="E47">A107</font></span></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th10</a>, <a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E22">C10</font></span></a></span>;<br/>
<a NAME="E47:18"/><span class="lab"><font color="Green" title="E50">A111</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">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#K11" title="AMI_3:func.11">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E48:18"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">i2</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:18"><span class="lab"><font color="Green" title="E45">A106</font></span></a>, <a class="txt" href="#E47:18"><span class="lab"><font color="Green" title="E50">A111</font></span></a>, <a class="ref" href="zfmisc_1.html#T7" title="ZFMISC_1:th.7">ZFMISC_1:7</a></span>;<br/>
<a NAME="E49:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A112</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">i2</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:18"><span class="lab"><font color="Green" title="E43">A104</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E50:18"/>
<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="ami_3.html#K12" title="AMI_3:func.12">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">i1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">i2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c20">T</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:18"><span class="lab"><font color="Green" title="E51">A112</font></span></a>, <a class="txt" href="#E35:18"><span class="lab"><font color="Green" title="E39">A99</font></span></a>, <a class="txt" href="#E46:18"><span class="lab"><font color="Green" title="E49">A109</font></span></a>, <a class="ref" href="funct_4.html#T85" title="FUNCT_4:th.85">FUNCT_4:85</a>, <a class="ref" href="relat_1.html#T151" title="RELAT_1:th.151">RELAT_1:151</a></span>;<br/>
<span class="kw">hence </span><a NAME="E51:18"/>
<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="c18">d</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c18">d</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:18"><span class="lab"><font color="Green" title="E38">A98</font></span></a>, <a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="ami_4.html#T9" target="_self" title="AMI_4:th.9">Th12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
