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<b>let </b><font color="Maroon">f</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>, <font color="Maroon">g</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="E1:27_1_2"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="seq_1.html#K1">.</a> <font color="Olive">i</font></span>)</span>
 <b>and </b><br/><a NAME="E2:27_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>  holds  <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="seq_1.html#K1">.</a> <font color="Olive">i</font></span>)</span>
 ;<br/>

<a NAME="E3:27_1_2"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:27_1_2_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>thus </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:27_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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