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<b>set </b><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c1">f</font> <a href="nat_3.html#K1" title="NAT_3:func.1">|^</a> <font color="Maroon" title="c2">a</font>;<br/>
<b>let </b><font color="Maroon" title="c4">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="seqm_3.html#D8" title="SEQM_3:def.8">SEQM_3:def 8</a><br/>

<b>assume </b><a NAME="E1:16_1_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="nat_3.html#K1" title="NAT_3:func.1">|^</a> <font color="Maroon" title="c2">a</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:16_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="nat_3.html#K1" title="NAT_3:func.1">|^</a> <font color="Maroon" title="c2">a</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="nat_3.html#K1" title="NAT_3:func.1">|^</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:16_1_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="nat_3.html#E3:16_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="nat_3.html#D1" target="_self" title="NAT_3:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E5:16_1_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>


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