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<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a> , <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="int_3.html#K1" target="_self">INT.Ring</a> ;<br/>

<b>assume </b><a NAME="E1:13_1_2"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">a'</font>, <font color="Olive">b'</font> being  <a href="int_1.html#NM1">Integer</a>  holds <br/>(  not <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or  not <font color="Olive">b'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or  not <font color="Olive">a'</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b'</font> )
 ;<br/>

<b>consider </b><font color="Maroon">a'</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">b'</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:13_1_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/>
<a NAME="E4:13_1_2"/>
not <font color="Maroon">a'</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:13_1_2"/>
 ex <font color="Olive">b'</font>, <font color="Olive">a'</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Olive">b'</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">a'</font> )
 <b>by </b><i/>;<br/>


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