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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>;<br/><b>let </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font> be    <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="E1:24"/><i><font color="Green" title="E17">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">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c3">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &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">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="scmring4.html#T16" target="_self" title="SCMRING4:th.16">Th16</a></i>;<br/>
<b>assume </b><a NAME="E2:24"/>
<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>
 ;<br/>

<a NAME="E3:24"/><b>then </b>
2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c3">j</font>
 
;<br/>
<b>hence </b><a NAME="E4:24"/>
 <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#E1:24"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


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