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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th31</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: NDIFF13:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">Z</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b4">g</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">E</font>,<span class="p1">(<span class="default"><a href="lopban_1.html#K16" title="LOPBAN_1:func.16">R_NormSpace_of_BoundedLinearOperators</a> (<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font>)</span>)</span>  st <span class="p1">(<span class="default"><font color="Olive" title="b4">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Z</font></span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b3">Z</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b5">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Z</font> holds <br/> for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b4">g</font>,<span class="p1">(<span class="default"><font color="Olive" title="b6">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b3">Z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b5">f</font>,<font color="Olive" title="b6">i</font>,<font color="Olive" title="b3">Z</font>)</div></div>
