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<div><span class="kw">theorem </span><a NAME="T8"><span class="comment"><font color="firebrick">:: TREES_2:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">W</font>, <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a><br/>  for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</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>   st <font color="Olive" title="b4">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b5">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp;  not <font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">q</font> <a href="xboole_0.html#R3" title="XBOOLE_0:pred.3">are_c=-comparable</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">W</font> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">W1</font>)</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b5">q</font>,<font color="Olive" title="b3">W2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">W</font> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b5">q</font>,<font color="Olive" title="b3">W2</font>)</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">W1</font>)</div></div>
