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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th31</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: TREES_1:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">T</font>, <font color="Olive" title="b3">T1</font> being   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>  st <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">T</font> holds <br/><font color="Olive" title="b2">T</font> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">T1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">t1</font> where <font color="Olive" title="b4">t1</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Olive" title="b2">T</font> :  not <font color="Olive" title="b1">p</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Olive" title="b4">t1</font> </span> } </span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b4">s</font></span>)</span> where <font color="Olive" title="b4">s</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Olive" title="b3">T1</font> : verum </span> } </span> </div></div>
