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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th49</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: TREES_3:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p</font> is  <a href="trees_3.html#V4" title="TREES_3:attr.4">Tree-yielding</a>  holds <br/>( <span class="p1">(<span class="default"><a href="trees_3.html#K11" title="TREES_3:func.11">tree</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">n</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> where <font color="Olive" title="b2">n</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font> </span> } </span>  &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font> holds <br/><span class="p1">(<span class="default"><a href="trees_3.html#K11" title="TREES_3:func.11">tree</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">n</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> ) )</div></div>
