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<b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="numbers.html#K1">REAL</a> , <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:34_1_2"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">i</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   holds <br/>( ( <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="newton.html#K2">|^</a> <font color="Olive">i</font> ) or ( not <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> 0 ) )
 <b>and </b><br/><a NAME="E2:34_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">i</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   holds <br/>( ( <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="newton.html#K2">|^</a> <font color="Olive">i</font> ) or ( not <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:34_1_2_1"/>
( ( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="newton.html#K2">|^</a> <font color="Maroon">i</font> ) or ( not <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:34_1_2_1"/>
<font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:34_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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