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<b>assume </b><a NAME="E1:30_1_1"/>
not  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default">0 <a href="nat_3.html#K4" target="_self">*</a> <font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<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="E3:30_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11">support</a> <span class="p1">(<span class="default">0 <a href="nat_3.html#K4" target="_self">*</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E4:30_1_1"/>
<span class="p1">(<span class="default">0 <a href="nat_3.html#K4" target="_self">*</a> <font color="Maroon">b</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</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="E5:30_1_1"/><b>then </b>
0 <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:30_1_1"/>
contradiction
 ;<br/>


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