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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th56</font></span>: <a NAME="T56"><span class="comment"><font color="firebrick">:: AOFA_000:56</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="freealg.html#V1" title="FREEALG:attr.1">disjoint_with_NAT</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">I</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> (<a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>,<font color="Olive" title="b1">X</font>)</span>)</span>  holds <br/>(  ex <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Olive" title="b3">x</font> or  ex <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ex <font color="Olive" title="b4">p</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> (<a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>,<font color="Olive" title="b1">X</font>)</span>)</span> st <br/>( <font color="Olive" title="b3">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 4 &amp; <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n</font> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Olive" title="b4">p</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">n</font> ) )</div></div>
