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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: PDIFF_1:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 1</span>)</span><br/>  for <font color="Olive" title="b2">J</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 1</span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K1" title="PDIFF_1:func.1">proj</a> (1,1)</span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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_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> 1</span>)</span> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">R</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">I</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">RestFunc</a> ) &amp; (  for <font color="Olive" title="b3">L</font> being   <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> 1</span>)</span> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">L</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">I</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LinearFunc</a> ) )</div></div>
