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<b>let </b><font color="Maroon">p</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><a NAME="E1:5"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">p</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">g</font>
 ;<br/>

<b>let </b><font color="Maroon">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:5"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">f1</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; <font color="Maroon">f1</font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> )
 <b>and </b><br/><a NAME="E3:5"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">f2</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> &amp; <font color="Maroon">f2</font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> )
 ;<br/>

<a NAME="E4:5"/><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_1_1"/>
( <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font> or <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1"><b>suppose </b></a><a NAME="E1:5_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x0</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:5_1_1_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Maroon">x0</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, , </i>;<br/><b>take </b><font color="Maroon">x0</font> = <font color="Maroon">x0</font>;<br/><b>thus </b><a NAME="E4:5_1_1_1"/>
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Maroon">x0</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_2"><b>suppose </b></a><a NAME="E1:5_1_1_2"/>
<font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font>
 ;<br/><div class="add"><a NAME="E2:5_1_1_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><b>set </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">f3</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="partfun2.html#K4">--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> as   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>, <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="funcop_1.html#T57">FUNCOP_1:57</a></i>;<br/><b>reconsider </b><font color="Maroon">f3</font> = <font color="Maroon">f3</font> as   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a>  ;<br/><b>reconsider </b><font color="Maroon">Z</font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> as  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  ;<br/><a NAME="E6:5_1_1_2"/><i><font color="Green">E46</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E7:5_1_1_2"/>
for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font></span>)</span> holds <br/><font color="Maroon">f3</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, </i>;<br/><a NAME="E8:5_1_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">f3</font> <a href="partfun2.html#R1">is_constant_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="partfun2.html#T76">PARTFUN2:76</a></i>;<br/><a NAME="E9:5_1_1_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">f3</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#T44">FCONT_1:44</a></i>;<br/><a NAME="E10:5_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">f3</font> <a href="partfun2.html#R1">is_constant_on</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, , <a class="ref" href="partfun2.html#T57">PARTFUN2:57</a></i>;<br/><a NAME="E11:5_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font>
 <b>by </b><i>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E12:5_1_1_2"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">f3</font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <font color="Maroon">Z</font> &amp; ( for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i>, <a class="ref" href="fdiff_1.html#T30">FDIFF_1:30</a></i>;<br/><b>set </b><font color="Maroon">f4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font>;<br/><b>set </b><font color="Maroon">f5</font> = <font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>;<br/><b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font>;<br/><a NAME="E13:5_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#T21">FCONT_1:21</a></i>;<br/><a NAME="E14:5_1_1_2"/><b>then </b>
<font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#T19">FCONT_1:19</a></i>;<br/><a NAME="E15:5_1_1_2"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#T19">FCONT_1:19</a></i>;<br/><a NAME="E16:5_1_1_2"/><i><font color="Green">E53</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/><a NAME="E17:5_1_1_2"/><i><font color="Green">E54</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#D2">FCONT_1:def 2</a></i>;<br/><a NAME="E18:5_1_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E19:5_1_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <font color="Maroon">Z</font> &amp; ( for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Olive">x</font></span>)</span> ) )
 <b>by </b><i>, <a class="ref" href="fdiff_1.html#T28">FDIFF_1:28</a></i>;<br/><a NAME="E20:5_1_1_2"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><a NAME="E21:5_1_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>;<br/><a NAME="E22:5_1_1_2"/><b>then </b><i><font color="Green">E58</font></i>: 
( <font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="fdiff_1.html#R2">is_differentiable_on</a> <font color="Maroon">Z</font> &amp; ( for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f3</font>,<font color="Olive">x</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>,<font color="Olive">x</font></span>)</span> ) )
 <b>by </b><i>, , <a class="ref" href="fdiff_1.html#T26">FDIFF_1:26</a></i>;<br/><a NAME="E23:5_1_1_2"/><i><font color="Green">E59</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font>
 <b>by </b><i>, <a class="ref" href="fcont_1.html#D2">FCONT_1:def 2</a></i>;<br/><a NAME="E24:5_1_1_2"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E25:5_1_1_2"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><a NAME="E26:5_1_1_2"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>;<br/><a NAME="E27:5_1_1_2"/><b>then </b><i><font color="Green">E61</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <font color="Maroon">Z</font> &amp; ( for <font color="Olive">x</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>,<font color="Olive">x</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Olive">x</font></span>)</span> ) )
 <b>by </b><i>, , <a class="ref" href="fdiff_1.html#T27">FDIFF_1:27</a></i>;<br/><a NAME="E28:5_1_1_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/><a NAME="E29:5_1_1_2"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E30:5_1_1_2"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>;<br/><a NAME="E31:5_1_1_2"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E32:5_1_1_2"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>;<br/><b>then </b><i><font color="Green">E65</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, </i>
<br/>.= 
0

;<br/><a NAME="E34:5_1_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i>, <a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/><a NAME="E35:5_1_1_2"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f3</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E36:5_1_1_2"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>;<br/><a NAME="E37:5_1_1_2"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E38:5_1_1_2"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D4">SEQ_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font>
<b>by </b><i/>
;<br/><b>then consider </b><font color="Maroon">x0</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E41:5_1_1_2"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp;  <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span>,<font color="Maroon">x0</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, , , </i>;<br/><b>take </b><font color="Maroon">x0</font> = <font color="Maroon">x0</font>;<br/> <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span>,<font color="Maroon">x0</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="seq_1.html#K7">-</a> <font color="Maroon">f1</font></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x0</font>
<b>by </b><i>, , <a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span>,<font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , , , <a class="ref" href="fdiff_1.html#T27">FDIFF_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f3</font> <a href="seq_1.html#K6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f3</font>,<font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>,<font color="Maroon">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , , , <a class="ref" href="fdiff_1.html#T26">FDIFF_1:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f3</font> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>,<font color="Maroon">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default">0 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span>,<font color="Maroon">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="fdiff_1.html#T30">FDIFF_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f2</font></span>)</span> <a href="fdiff_1.html#K2">`|</a> <font color="Maroon">Z</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Maroon">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="fdiff_1.html#T28">FDIFF_1:28</a></i>
;<br/><a NAME="E43:5_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T15">XCMPLX_1:15</a></i>;<br/><b>hence </b><a NAME="E44:5_1_1_2"/>
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Maroon">x0</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Maroon">x0</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:5"/>
 ex <font color="Olive">x0</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">x0</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">g</font></span><a href="rcomp_1.html#K2">.[</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f2</font>,<font color="Olive">x0</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">g</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">f1</font>,<font color="Olive">x0</font></span>)</span> )
 ;<br/>


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