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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E15">Def4</font></span>   defines <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <a onclick="hs(this)" href="javascript:()">INTEGRA5:def 4 : <br/></a><span> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( ( <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> implies  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> (<font color="Olive" title="b3">f</font>,<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>) ) &amp; (  not <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> implies  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> (<font color="Olive" title="b3">f</font>,<span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>)</span>)</span> ) );<br/></span></div>
