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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">:: NDIFF_6:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b4">Z</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <span class="p1">(<span class="default"><a href="ndiff_6.html#K5" title="NDIFF_6:func.5">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">Z</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">Z</font> &amp; <span class="p1">(<span class="default"><a href="ndiff_6.html#K5" title="NDIFF_6:func.5">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">Z</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">Z</font></span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b4">Z</font> &amp; <span class="p1">(<span class="default"><a href="ndiff_6.html#K5" title="NDIFF_6:func.5">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">Z</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">Z</font></span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b4">Z</font></span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b4">Z</font> )</div></div>
