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<b>set </b><font color="Maroon">g</font> = <font color="Maroon">f</font> <a href="nat_3.html#K1" target="_self">|^</a> <font color="Maroon">a</font>;<br/>
<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a><br/>

<b>assume </b><a NAME="E1:16_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="nat_3.html#K1" target="_self">|^</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:16_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="nat_3.html#K1" target="_self">|^</a> <font color="Maroon">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="nat_3.html#K1" target="_self">|^</a> <font color="Maroon">a</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:16_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span> <a href="newton.html#K3">|^</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:16_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>


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