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<b>thus </b><a NAME="E1:1_1_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <a href="int_3.html#K1">INT.Ring</a>  is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="int_3.html#D3">INT_3:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a><br/>

<b>thus </b><a NAME="E2:1_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="int_3.html#K1">INT.Ring</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_2.html#T6">AMI_2:6</a>, <a class="ref" href="int_3.html#D3">INT_3:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="scmring1.html#D2">SCMRING1:def 2</a><br/>

<b>assume </b><a NAME="E3:1_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="int_3.html#K1">INT.Ring</a>  <a href="hidden.html#R1">=</a>  <a href="scmring1.html#K1">SCM-Instr</a> <a href="int_3.html#K1">INT.Ring</a> 
 ;<br/>

<a NAME="E4:1_1_1"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="scmring1.html#K1">SCM-Instr</a> <a href="int_3.html#K1">INT.Ring</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a>, <a class="ref" href="int_3.html#D3">INT_3:def 3</a></i>;<br/>
<a NAME="E5:1_1_1"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="gr_cy_1.html#K1">Segm</a> 8 &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="int_3.html#K1">INT.Ring</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a>  &amp; 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_1.html#T2">AMI_1:2</a></i>;<br/>


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