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<div><div><a NAME="S1"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: TREES_1:sch 1</font></span><br/></a><span class="lab"><font color="Green" title="E1">TreeInd</font></span>{ <font color="Maroon">P<sub>1</sub></font>[  <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>] } :<br/><div class="add"><a NAME="E2:68"/>
 for <font color="Olive" title="b1">fT</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">fT</font>]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:68"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
 for <font color="Olive" title="b1">fT</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>  st (  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 <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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">fT</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">fT</font> <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>] ) holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">fT</font>]
 </div></div></div>
