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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:65"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E2:65"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></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="E3:65"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></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="E4:65"/><b>then </b>
( ( <font color="Maroon">c<sub>1</sub></font> is  <a href="finset_1.html#V1">finite</a> <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">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="trees_3.html#V2" target="_self">constituted-FinTrees</a> ) &amp; (  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="trees_3.html#V2" target="_self">constituted-FinTrees</a> implies <font color="Maroon">c<sub>1</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V5" target="_self">FinTree-yielding</a> implies  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="trees_3.html#V2" target="_self">constituted-FinTrees</a> ) &amp; (  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="trees_3.html#V2" target="_self">constituted-FinTrees</a> implies <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V5" target="_self">FinTree-yielding</a> ) )
 
<b>by </b><i><a class="ref" href="trees_3.html#D10" target="_self">Def10</a>, <a class="ref" href="trees_3.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E5:65"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K2">|-&gt;</a> <font color="Maroon">c<sub>1</sub></font> is <a href="trees_3.html#V5" target="_self">FinTree-yielding</a> iff <font color="Maroon">c<sub>1</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="trees_1.html#NM1">Tree</a> )
 ;<br/>


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