<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><br/>



<a NAME="E1:30"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T17" onmouseover="rs('xxreal_0/T17')" onmouseout="rh()">XXREAL_0:17</a></span>;<br/>
<a NAME="E2:30"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
;<br/>
<a NAME="E3:30"/>
( <a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a>  &amp; <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#T25" onmouseover="rs('fdiff_1/T25')" onmouseout="rh()">FDIFF_1:25</a>, <a class="ref" href="taylor_1.html#T16" onmouseover="rs('taylor_1/T16')" onmouseout="rh()">TAYLOR_1:16</a>, <a class="ref" href="xxreal_0.html#T25" onmouseover="rs('xxreal_0/T25')" onmouseout="rh()">XXREAL_0:25</a></span>;<br/>
<a NAME="E4:30"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:30"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="integra7.html#T20" target="_self" onmouseover="rs('integra7/T20')" onmouseout="rh()">Th20</a>, <a class="ref" href="integra7.html#T27" target="_self" onmouseover="rs('integra7/T27')" onmouseout="rh()">Th27</a>, <a class="ref" href="sin_cos.html#T47" onmouseover="rs('sin_cos/T47')" onmouseout="rh()">SIN_COS:47</a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E5:30"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> implies <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="30_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:30_1"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span><br/>

<a NAME="E2:30_1"/><span class="kw">then </span>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T36" onmouseover="rs('xxreal_0/T36')" onmouseout="rh()">XXREAL_0:36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:30_1"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E1:30_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:30"/>
(  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> implies <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="30_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:30_2"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span><br/>

<a NAME="E2:30_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A7</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T36" onmouseover="rs('xxreal_0/T36')" onmouseout="rh()">XXREAL_0:36</a></span>;<br/>
<a NAME="E3:30_2"/>
( <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font> implies <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="30_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:30_2_1"/>
<font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span><br/>

<a NAME="E2:30_2_1"/><span class="kw">then </span>
 <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">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> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="integra5.html#D4" onmouseover="rs('integra5/D4')" onmouseout="rh()">INTEGRA5:def 4</a></span>;<br/>
<a NAME="E3:30_2_1"/><span class="kw">then </span>
<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E1:30_2"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E2:30_2"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="integra5.html#D4" onmouseover="rs('integra5/D4')" onmouseout="rh()">INTEGRA5:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:30_2_1"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:30_2"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E5:30"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E1:30_2"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:30"/>
 <a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> (<a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">exp_R</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:30"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T15" onmouseover="rs('xxreal_0/T15')" onmouseout="rh()">XXREAL_0:15</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
