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<span class="kw">thus </span><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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#D3" title="INT_3:def.3">INT_3:def 3</a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><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> 
 <span class="kw">by</span> <span class="lab"><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></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="scmring1.html#D2" title="SCMRING1:def.2">SCMRING1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E1">X</font></span>: 
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> 
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<a NAME="E5:1_1_1"/><span class="lab"><font color="Green" title="E2">W</font></span>: 
 <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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p3">(<span class="default"><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>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring1.html#T21" title="SCMRING1:th.21">SCMRING1:21</a></span>;<br/>
<a NAME="E6:1_1_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p3">(<span class="default"><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>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:1_1_1"><span class="lab"><font color="Green" title="E2">W</font></span></a>, <a class="txt" href="#E4:1_1_1"><span class="lab"><font color="Green" title="E1">X</font></span></a></span>;<br/>
<a NAME="E7:1_1_1"/><span class="kw">then </span>
 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>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><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>)</span> &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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:1_1_1"/>
contradiction
 ; <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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