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<b>let </b><font color="Maroon" title="c4">it1</font>, <font color="Maroon" title="c5">it2</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:72_1_2"/><i><font color="Green" title="E36">A6</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c4">it1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="Olive" title="b1">x</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Olive" title="b1">x</font></span>)</span>
 <b>and </b><br/><a NAME="E2:72_1_2"/><i><font color="Green" title="E37">A7</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c5">it2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="Olive" title="b1">x</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Olive" title="b1">x</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:72_1_2_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ;<br/><b>thus </b><font color="Maroon" title="c4">it1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<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="c6">x</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">.</a> <font color="Maroon" title="c6">x</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E1:72_1_2"><i><font color="Green" title="E36">A6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">it2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="polynom1.html#E2:72_1_2"><i><font color="Green" title="E37">A7</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:72_1_2"/>
<font color="Maroon" title="c4">it1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">it2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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