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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b1</font> be  <a href="seqm_3.html#V6">natural-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>, <font color="Maroon">b2</font> be  <a href="seqm_3.html#V6">natural-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>;<br/>



<b>thus </b><a NAME="E1:92"/>
 <a href="polynom1.html#K11" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">b2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K11" target="_self">support</a> <font color="Maroon">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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="E1:92_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" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">b2</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:92_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K11" target="_self">support</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E3:92_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="polynom1.html#E1:92_1"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E4:92_1"/>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">x</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="nat_2.html#T10">NAT_2:10</a></i>;<br/>
<a NAME="E5:92_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K10" target="_self">-'</a> <font color="Maroon">b2</font></span>)</span> <a href="polynom1.html#K8" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:92_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="polynom1.html#E1:92_1"><i><font color="Green">E41</font></i></a></i>;<br/>


</div><b>end;</b></div>


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