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<b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="partfun1.html#V1">total</a>  <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s0</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>;<br/>





<b>consider </b><font color="Maroon">pai</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">S</font><b> such that </b><br/><a NAME="E2:140"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">s0</font>
 <b>and </b><br/><a NAME="E3:140"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Olive">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">pai</font> = <font color="Maroon">pai</font> as    <a href="modelc_1.html#M1" target="_self">inf_path</a> of <font color="Maroon">R</font> <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">pai</font>
;<br/>

<b>thus </b><a NAME="E5:140"/>
<font color="Maroon">pai</font> <a href="funct_2.html#K3">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">s0</font>
 <b>by </b><i/>;<br/>


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