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<b>set </b><font color="Maroon">f</font> =  <a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</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="E1:40_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"><a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</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="E3:40_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font></span>)</span>
 <b>and </b><br/><a NAME="E4:40_1_1"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</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="E5:40_1_1"/>
( <font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> or <font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> )
 
;<br/>
<a NAME="E6:40_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> or <span class="p1">(<span class="default"><a href="nat_3.html#K6" target="_self">max</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:40_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/>;<br/>


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