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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:64"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E2:64"/><b>then </b>
( <font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">x</font> &amp;  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a>, <a class="ref" href="finseq_2.html#D2">FINSEQ_2:def 2</a></i>;<br/>
<a NAME="E3:64"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E4:64"/><b>then </b>
( ( <font color="Maroon">x</font> is   <a href="trees_1.html#NM1">Tree</a> implies  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font></span>)</span> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a> ) &amp; (  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font></span>)</span> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a> implies <font color="Maroon">x</font> is   <a href="trees_1.html#NM1">Tree</a> ) &amp; ( <font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font> is <a href="trees_3.html#V4" target="_self">Tree-yielding</a> implies  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font></span>)</span> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a> ) &amp; (  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font></span>)</span> is <a href="trees_3.html#V1" target="_self">constituted-Trees</a> implies <font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font> is <a href="trees_3.html#V4" target="_self">Tree-yielding</a> ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:64"/>
( <font color="Maroon">i</font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">x</font> is <a href="trees_3.html#V4" target="_self">Tree-yielding</a> iff <font color="Maroon">x</font> is   <a href="trees_1.html#NM1">Tree</a> )
 ;<br/>


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