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<b>thus </b><a NAME="E1:1_1_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="int_3.html#D3" title="INT_3:def.3">INT_3:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a></span><br/>

<b>thus </b><a NAME="E2:1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="int_3.html#D3" title="INT_3:def.3">INT_3:def 3</a>, <a class="ref" href="numbers.html#T27" title="NUMBERS:th.27">NUMBERS:27</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="scmring1.html#D2" title="SCMRING1:def.2">SCMRING1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> </span><br/>

<b>assume </b><a NAME="E3:1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:1_1_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a>, <a class="ref" href="int_3.html#D3" title="INT_3:def.3">INT_3:def 3</a></i>;<br/>
<a NAME="E5:1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  &amp; 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:1_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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