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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: HALLMAR1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">i</font>, <font color="Olive" title="b4">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b5">B</font> being    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">i</font><br/>  for <font color="Olive" title="b6">C</font> being    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Olive" title="b5">B</font>,<font color="Olive" title="b4">j</font>  st <font color="Olive" title="b3">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="b2">A</font> &amp; <font color="Olive" title="b4">j</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="b2">A</font> &amp; <font color="Olive" title="b6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>( <font color="Olive" title="b6">C</font> is    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">j</font> &amp; <font color="Olive" title="b6">C</font> is    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">i</font> )</div></div>
