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<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">j</font> holds <br/> <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Olive" title="b2">j</font></span><br/><b>let </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> implies  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c3">j</font> )</span><br/>



<a NAME="E1:7"/><i><font color="Green" title="E4">A1</font></i>: 
(  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,<font color="Maroon" title="c3">j</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,<font color="Maroon" title="c2">i</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 
<b>by </b><i><a class="ref" href="scmring4.html#T3" target="_self" title="SCMRING4:th.3">Th16</a></i>;<br/>
<b>assume </b><a NAME="E2:7"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c3">j</font></span><br/>

<b>hence </b><a NAME="E3:7"/>
 <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmring3.html#K2" title="SCMRING3:func.2">dl.</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c3">j</font>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:7"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>; <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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