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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: MODAL_1:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Z1</font>, <font color="Olive" title="b2">Z2</font> being   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a><br/>  for <font color="Olive" title="b3">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>   st <font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Z1</font> holds <br/> for <font color="Olive" title="b4">v</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Olive" title="b1">Z1</font> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">Z2</font>)<br/>  for <font color="Olive" title="b5">w</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Olive" title="b2">Z2</font>  st <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b5">w</font> holds <br/> <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Olive" title="b4">v</font>, <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <font color="Olive" title="b5">w</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_2.html#T37" onmouseover="rs('trees_2/T37')" onmouseout="rh()">TREES_2:37</a></span>;<br/></div></div>
