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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">h</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<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> ;<br/>





<span class="p1"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">h</font></span>)</span>,<font color="Maroon" title="c1">x</font></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></span> = 
<span class="p1"><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="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">h</font></span>)</span></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</a></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"><a href="diff_1.html#K6" title="DIFF_1:func.6">bD</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">h</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">h</font>
<b>by </b><i><a class="ref" href="diff_1.html#T4" title="DIFF_1:th.4">DIFF_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="diff_1.html#K5" title="DIFF_1:func.5">bD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="diff_1.html#NK12" title="DIFF_1:NK.12">bdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c2">h</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">h</font>
<b>by </b><i><a class="ref" href="diff_1.html#D7" title="DIFF_1:def.7">DIFF_1:def 7</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#NK12" title="DIFF_1:NK.12">bdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">h</font></span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">h</font>
<b>by </b><i><a class="ref" href="diff_1.html#D7" title="DIFF_1:def.7">DIFF_1:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E2:3"/>
<span class="p1"><a href="diff_1.html#K12" title="DIFF_1:func.12">[!</a><span class="default"><font color="Maroon" title="c3">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c2">h</font></span>)</span>,<font color="Maroon" title="c1">x</font></span><a href="diff_1.html#K12" title="DIFF_1:func.12">!]</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#NK12" title="DIFF_1:NK.12">bdif</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">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="c1">x</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">h</font>
 ;<br/>


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