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<span class="kw">set </span><font color="Maroon" title="c3">s</font> = <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>;<br/>
<a NAME="E1:8_1_1"/><span class="lab"><font color="Green" title="E1">A2</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
;<br/>
<a NAME="E2:8_1_1"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D3" title="AMI_1:def.3">AMI_1:def 3</a></span>;<br/>
<a NAME="E3:8_1_1"/><span class="kw">then </span>
 <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 <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E1">A2</font></span></a></span>;<br/>
<a NAME="E4:8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E2">A3</font></span>: 
 <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> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">l</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as    <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>  ;<br/>
<a NAME="E6:8_1_1"/>
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font>
 
;<br/>
<a NAME="E7:8_1_1"/><span class="kw">then </span>
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D14" title="AMI_1:def.14">AMI_1:def 14</a></span>;<br/>
<a NAME="E8:8_1_1"/><span class="kw">then </span>
<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K8" title="CARD_3:func.8">sproduct</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8_1_1"><span class="lab"><font color="Green" title="E2">A3</font></span></a>, <a class="ref" href="card_3.html#T76" title="CARD_3:th.76">CARD_3:76</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">s</font> = <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> ;<br/>
<a NAME="E10:8_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#D5" title="AFINSQ_1:def.5">AFINSQ_1:def 5</a></span>;<br/>
<a NAME="E11:8_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T87" title="CARD_1:th.87">CARD_1:87</a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:8_1_1"/>
<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> is   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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