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<b>let </b><font color="Maroon">it1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">it2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">it1</font> <a href="jordan1h.html#R1">is_sufficiently_large_for</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:3_1_2"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="jordan1h.html#R1">is_sufficiently_large_for</a> <font color="Maroon">C</font> holds <br/><font color="Olive">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">it1</font>
 <b>and </b><br/><a NAME="E3:3_1_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">it2</font> <a href="jordan1h.html#R1">is_sufficiently_large_for</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E4:3_1_2"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="jordan1h.html#R1">is_sufficiently_large_for</a> <font color="Maroon">C</font> holds <br/><font color="Olive">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">it2</font>
 ;<br/>

<a NAME="E5:3_1_2"/>
( <font color="Maroon">it1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">it2</font> &amp; <font color="Maroon">it2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">it1</font> )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E6:3_1_2"/>
<font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">it2</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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