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<b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> ;<br/>

<b>assume </b><a NAME="E1:13_1_2"/><i><font color="Green" title="E8">A1</font></i>: 
for <font color="Olive" title="b1">a'</font>, <font color="Olive" title="b2">b'</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  holds <br/>(  not <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> or  not <font color="Olive" title="b2">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> or  not <font color="Olive" title="b1">a'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b'</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">a'</font>, <font color="Maroon" title="c7">b'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:13_1_2"/><i><font color="Green" title="E9">A2</font></i>: 
( <font color="Maroon" title="c6">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Maroon" title="c7">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> )
 ;<br/>
<a NAME="E4:13_1_2"/>
not <font color="Maroon" title="c6">a'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">b'</font>
 
<b>by </b><i><a class="txt" href="int_3.html#E1:13_1_2"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="int_3.html#E3:13_1_2"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:13_1_2"/>
 ex <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">a'</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Olive" title="b1">b'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">a'</font> )
 <b>by </b><i><a class="txt" href="int_3.html#E3:13_1_2"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/>


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