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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="seq_1.html#V1">real-yielding</a> <a href="polynom1.html#V1">finite-support</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="nat_3.html#K5" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></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><br/>

<b>assume </b><a NAME="E1:36"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#K5" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="nat_3.html#K5" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/>
<a NAME="E3:36"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
;<br/>
<a NAME="E4:36"/><b>then </b>
( <span class="p1">(<span class="default"><a href="nat_3.html#K5" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> or <span class="p1">(<span class="default"><a href="nat_3.html#K5" target="_self">min</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_3.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="nat_3.html#E2:36"><i><font color="Green">E18</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11">support</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11">support</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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