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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">ThL8</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: MSAFREE5:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b2">c</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">d</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><br/>  for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="trees_3.html#V6" title="TREES_3:attr.6">DTree-yielding</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">p</font> &amp; (  for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b7">d1</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">p</font> &amp; <font color="Olive" title="b7">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> holds <br/><font color="Olive" title="b5">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b7">d1</font>,<font color="Olive" title="b2">c</font>) <a href="trees_4.html#K9" title="TREES_4:func.9">&lt;-</a> <font color="Olive" title="b3">d</font> ) holds <br/>(<span class="p1">(<span class="default"><font color="Olive" title="b1">b</font> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Olive" title="b4">p</font></span>)</span>,<font color="Olive" title="b2">c</font>) <a href="trees_4.html#K9" title="TREES_4:func.9">&lt;-</a> <font color="Olive" title="b3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Olive" title="b5">q</font></div></div>
