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<b>let </b><font color="Maroon">b3</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">X</font>, <font color="Maroon">b4</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:4_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b3</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 ;<br/>

<b>assume </b><a NAME="E2:4_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">b2</font> <a href="polynom1.html#K9">+</a> <font color="Maroon">b4</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font>
 ;<br/>

<i><font color="Green">E35</font></i>:  <a href="relat_1.html#K1">dom</a> <font color="Maroon">b3</font> = 
<font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">b4</font>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:4_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">b3</font>
 ;<br/><b>thus </b><font color="Maroon">b3</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K8">.</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">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">b4</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
<font color="Maroon">b4</font> <a href="polynom1.html#K8">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:4_1_1"/>
<font color="Maroon">b3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b4</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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