<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">b1</font>, <font color="Maroon" title="c3">b2</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="109_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">k</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:109_1"/>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D6" target="_self" title="POLYNOM1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D5" target="_self" title="POLYNOM1:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c4">k</font>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:109"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c2">b1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">b2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


</div>
