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<b>set </b><font color="Maroon">f</font> =  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="mboolean.html#K1">bool</a> <font color="Maroon">M</font></span>)</span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>1</sub></font> is    <a href="osalg_2.html#M1" target="_self">OrderSortedSubset</a> of <font color="Maroon">M</font>;<br/>
<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:29_1_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="mboolean.html#K1">bool</a> <font color="Maroon">M</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

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

<b>thus </b><a NAME="E3:29_1_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">y</font> is    <a href="osalg_2.html#M1" target="_self">OrderSortedSubset</a> of <font color="Maroon">M</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E4:29_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">y</font> is    <a href="osalg_2.html#M1" target="_self">OrderSortedSubset</a> of <font color="Maroon">M</font>
 ;<br/>

<a NAME="E5:29_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="mboolean.html#K1">bool</a> <font color="Maroon">M</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:29_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>


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