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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th11</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: LPSPACE1:11</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>, <font color="Olive" title="b4">h</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="rfunct_3.html#K13" title="RFUNCT_3:func.13">addpfunc</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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K13" title="RFUNCT_3:func.13">addpfunc</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="b4">h</font>)</span>)</span>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K13" title="RFUNCT_3:func.13">addpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfunct_3.html#K13" title="RFUNCT_3:func.13">addpfunc</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>)</span>)</span>,<font color="Olive" title="b4">h</font>) <span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#T15" onmouseover="rs('rfunct_3/T15')" onmouseout="rh()">RFUNCT_3:15</a>, <a class="ref" href="binop_1.html#D3" onmouseover="rs('binop_1/D3')" onmouseout="rh()">BINOP_1:def 3</a></span>;<br/></div></div>
