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<b>let </b><font color="Maroon">it1</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>, <font color="Maroon">it2</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:72_1_2"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds  <font color="Maroon">it1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Olive">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="seq_1.html#K1">.</a> <font color="Olive">x</font></span>)</span>
 <b>and </b><br/><a NAME="E2:72_1_2"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds  <font color="Maroon">it2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Olive">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="seq_1.html#K1">.</a> <font color="Olive">x</font></span>)</span>
 ;<br/>

<a NAME="E3:72_1_2"/><i><font color="Green">E69</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:72_1_2"/><i><font color="Green">E70</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</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="72_1_2_1"><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="E1:72_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>thus </b><font color="Maroon">it1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">it2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:72_1_2"/>
<font color="Maroon">it1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">it2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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