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<b>let </b><font color="Maroon" title="c1">h</font>, <font color="Maroon" title="c2">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Maroon" title="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:2"/>
<font color="Maroon" title="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span><br/>

<a NAME="E2:2"/><b>then </b>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span> &amp; <font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span> )
 
;<br/>
<a NAME="E3:2"/><b>then </b><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font>,<font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<a NAME="E4:2"/><i><font color="Green" title="E3">A2</font></i>: 
<span class="p1">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1 is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<b>by </b><i><a class="ref" href="diff_1.html#T2" title="DIFF_1:th.2">DIFF_1:2</a></i>;<br/>
<span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span> = 
<span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<font color="Maroon" title="c2">x</font></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span>
<b>by </b><i><a class="txt" href="#E3:2"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="diff_1.html#T34" title="DIFF_1:th.34">DIFF_1:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<font color="Maroon" title="c2">x</font></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="diff_1.html#T29" title="DIFF_1:th.29">DIFF_1:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="diff_1.html#T29" title="DIFF_1:th.29">DIFF_1:29</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"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="diff_2.html#T1" target="_self" title="DIFF_2:th.1">Th1</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"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</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"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="diff_2.html#T1" target="_self" title="DIFF_2:th.1">Th1</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"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#K3" title="DIFF_1:func.3">fD</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="diff_1.html#T3" title="DIFF_1:th.3">DIFF_1:3</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"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">h</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span>
<b>by </b><i><a class="ref" href="diff_1.html#D6" title="DIFF_1:def.6">DIFF_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T79" title="XCMPLX_1:th.79">XCMPLX_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E6:2"/>
<span class="p1"><a href="diff_1.html#K13" title="DIFF_1:func.13">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c1">h</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span></span><a href="diff_1.html#K13" title="DIFF_1:func.13">!]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="diff_1.html#NK10" title="DIFF_1:NK.10">fdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c1">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> 2</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">h</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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