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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th52</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: INTEGR19:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being    <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">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b6">E</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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><br/>  for <font color="Olive" title="b7">f</font> being   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<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>  st <font color="Olive" title="b2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">b</font> &amp; <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b7">f</font> &amp; (  for <font color="Olive" title="b8">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> holds <br/><font color="Olive" title="b7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">E</font> ) &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Olive" title="b5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> holds <br/> <a href="integr18.html#K6" title="INTEGR18:func.6">integral</a> (<font color="Olive" title="b7">f</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">d</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b4">c</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b6">E</font></div></div>
