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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E50">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: ALGSTR_4:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b5">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b3">Z</font>  st <font color="Olive" title="b2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Z</font> &amp; <font color="Olive" title="b4">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">g</font> holds <br/> <a href="algstr_4.html#K18" title="ALGSTR_4:func.18">free_magmaF</a> <font color="Olive" title="b4">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="algstr_4.html#K18" title="ALGSTR_4:func.18">free_magmaF</a> <font color="Olive" title="b5">g</font></div></div>
