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<b>let </b><font color="Maroon">T</font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">T1</font> be   <a href="trees_1.html#NM1">Tree</a>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="trees_1.html#M4">AntiChain_of_Prefixes</a> of <font color="Maroon">T</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:7_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:7_1"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="trees_1.html#D14">TREES_1:def 14</a></i>;<br/><b>then consider </b><font color="Maroon">q</font> being    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:7_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/><a NAME="E5:7_1"/>
 <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">T1</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T47">TREES_1:47</a></i>;<br/><b>then consider </b><font color="Maroon">s'</font> being    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T1</font><b> such that </b><br/><a NAME="E7:7_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">s'</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K5">NAT</a> 
 ;<br/><a NAME="E8:7_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">s'</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/><b>hence </b><a NAME="E9:7_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">p</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font>, <font color="Olive">s</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T1</font> : <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:7"/>
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">p</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">p</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T</font>, <font color="Olive">s</font> is    <a href="trees_1.html#M1">Element</a> of <font color="Maroon">T1</font> : <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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