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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: NDIFF_4:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">J</font> being   <a href="struct_0.html#NM4" title="STRUCT_0:NM.4">Function</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> 1</span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">J</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pdiff_1.html#K1" title="PDIFF_1:func.1">proj</a> (1,1) holds <br/>( (  for <font color="Olive" title="b3">R</font> being   <a href="ndiff_3.html#NM1" title="NDIFF_3:NM.1">RestFunc</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span> holds  <font color="Olive" title="b3">R</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">J</font> is   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">RestFunc</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span> ) &amp; (  for <font color="Olive" title="b3">L</font> being   <a href="ndiff_3.html#NM2" title="NDIFF_3:NM.2">LinearFunc</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span> holds  <font color="Olive" title="b3">L</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b2">J</font> is   <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 <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span> ) )</div></div>
