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<b>let </b><font color="Maroon">n1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>given </b><font color="Maroon">X1</font> being    <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font><b> such that </b><a NAME="E1:67_2_2"/><i><font color="Green">E95</font></i>: 
( <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X1</font> &amp; ( for <font color="Olive">Y</font> being   <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font> holds   <a href="card_1.html#K4">card</a> <font color="Olive">Y</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X1</font> ) )
 ;<br/>

<b>given </b><font color="Maroon">X2</font> being    <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font><b> such that </b><a NAME="E2:67_2_2"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X2</font> &amp; ( for <font color="Olive">Y</font> being   <a href="trees_1.html#M4" target="_self">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font> holds   <a href="card_1.html#K4">card</a> <font color="Olive">Y</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X2</font> ) )
 ;<br/>

<a NAME="E3:67_2_2"/>
(  <a href="card_1.html#K4">card</a> <font color="Maroon">X1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X2</font> &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">X2</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">X1</font> )
 
<b>by </b><i><a class="ref" href="trees_1.html#T6" target="_self">Th6</a>, <a class="ref" href="trees_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:67_2_2"/>
<font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n2</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T6" target="_self">Th6</a>, <a class="ref" href="trees_1.html#D1" target="_self">Def1</a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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