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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th22</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: NDIFF13:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b4">L</font> being   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">Lipschitzian</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font> holds <br/> (  <a href="ndiff13.html#K2" title="NDIFF13:func.2">LTRN</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b4">L</font>,<font color="Olive" title="b1">E</font>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">L</font> &amp; (  for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b6">V</font> being   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">Lipschitzian</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">E</font>,<span class="p1">(<span class="default"><a href="ndiff_6.html#K3" title="NDIFF_6:func.3">diff_SP</a> (<font color="Olive" title="b5">i</font>,<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font>)</span>)</span> holds  <span class="p1">(<span class="default"><a href="ndiff13.html#K2" title="NDIFF13:func.2">LTRN</a> (<span class="p2">(<span class="default"><font color="Olive" title="b5">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b4">L</font>,<font color="Olive" title="b1">E</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ndiff13.html#K2" title="NDIFF13:func.2">LTRN</a> (<font color="Olive" title="b5">i</font>,<font color="Olive" title="b4">L</font>,<font color="Olive" title="b1">E</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b6">V</font> ) )</div></div>
