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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">J</font> be  <a href="waybel_3.html#V4">non-Empty</a> <a href="waybel18.html#V1">TopSpace-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:18"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="waybel18.html#K2">product_prebasis</a> <font color="Maroon">J</font>
 ;<br/>

<b>then consider </b><font color="Maroon">i</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">T</font> being    <a href="pre_topc.html#L1">TopStruct</a> , <font color="Maroon">Ai</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:18"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">Ai</font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E5:18"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>and </b><br/><a NAME="E6:18"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">J</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">Ai</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel18.html#D2">WAYBEL18:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">i</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">i</font>
;<br/>

<b>reconsider </b><font color="Maroon">Ai</font> = <font color="Maroon">Ai</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="waybel18.html#K4">.</a> <font color="Maroon">i</font></span>)</span> <b>by </b><i><a class="txt" href="yellow17.html#E3:18"><i><font color="Green">E20</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">Ai</font>
;<br/>

<b>thus </b><a NAME="E9:18"/>
<font color="Maroon">Ai</font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i>, <a class="txt" href="yellow17.html#E3:18"><i><font color="Green">E20</font></i></a></i>;<br/>

<b>thus </b><a NAME="E10:18"/>
<span class="p1">(<span class="default"><a href="waybel18.html#K6">proj</a> <font color="Maroon">J</font>,<font color="Maroon">i</font></span>)</span> <a href="relset_1.html#K11">"</a> <font color="Maroon">Ai</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="waybel18.html#T5">WAYBEL18:5</a></i>;<br/>


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