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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: WELLSET1:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st (  for <font color="Olive" title="b3">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">D</font> holds <br/>(  not <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> &amp; <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">D</font> ) ) holds <br/> ex <font color="Olive" title="b3">R</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> st <br/>(  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">D</font> &amp; <font color="Olive" title="b3">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp;  not  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b3">R</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">D</font> &amp; (  for <font color="Olive" title="b4">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b3">R</font> holds <br/>( <font color="Olive" title="b3">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">D</font> &amp; <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">R</font> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Olive" title="b4">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y</font> ) ) )</div></div>
