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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th4</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: FUZZY_8:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">d</font> holds <br/>(  <a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="fcont_1.html#K1" title="FCONT_1:func.1">AffineMap</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span></span>)</span>,<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">d</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p0">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><font color="Olive" title="b3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">b</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span></span>)</span> &amp;  <a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> (<span class="p1">(<span class="default"><a href="fcont_1.html#K1" title="FCONT_1:func.1">AffineMap</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span>,<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b4">d</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">b</font></span>)</span> )</div></div>
