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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>2</sub></font> is    <a href="pralg_2.html#M2">MSAlgebra-Family</a> of <font color="Maroon">J</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">S</font>;<br/>
<a NAME="E1:38_1_1"/><i><font color="Green">E38</font></i>: 
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">I</font> holds <br/> ex <font color="Olive">F</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Olive">F</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_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="E1:38_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>consider </b><font color="Maroon">F</font> being    <a href="pralg_2.html#M2">MSAlgebra-Family</a> of <font color="Maroon">J</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">S</font>;<br/>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E3:38_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">i</font>,<font color="Maroon">F</font>]
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">C</font> being    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font><b> such that </b><br/><a NAME="E3:38_1_1"/><i><font color="Green">E41</font></i>: 
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">I</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>]
 <b>from </b><i><a class="ref" href="pboole.html#S3">PBOOLE:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon">C</font>
;<br/>

<b>thus </b><a NAME="E4:38_1_1"/>
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">I</font> holds <br/><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> is    <a href="pralg_2.html#M2">MSAlgebra-Family</a> of <font color="Maroon">J</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Maroon">S</font>
 <b>by </b><i/>;<br/>


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