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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: LPSPACE1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</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="b2">f</font>, <font color="Olive" title="b3">g</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Olive" title="b1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>) holds  <span class="p1">(<span class="default"><a href="lpspace1.html#K3" title="LPSPACE1:func.3">multpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="lpspace1.html#K3" title="LPSPACE1:func.3">multpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Olive" title="b3">g</font>,<font color="Olive" title="b2">f</font>)</div></div>
