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<b>let </b><font color="Maroon">f</font> be  <a href="pencil_1.html#V11" target="_self">TopStruct-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:31_3_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f</font> is <a href="pencil_1.html#V15" target="_self">PLS-yielding</a>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D18" target="_self">PENCIL_1:def 18</a><br/>

<b>assume </b><a NAME="E2:31_3_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">S1</font> = <font color="Maroon">x</font> as  non <a href="struct_0.html#V3">empty</a> non <a href="pencil_1.html#V3" target="_self">void</a> <a href="pencil_1.html#V5" target="_self">with_non_trivial_blocks</a>  <a href="pre_topc.html#L1">TopStruct</a>  <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">s</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:31_3_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">s</font> as   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">S1</font> <b>by </b><i/>;<br/>
<a NAME="E7:31_3_1"/>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">s</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">s1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">s2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:31_3_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">s1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s2</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E10:31_3_1"/>
<font color="Maroon">x</font> is  non <a href="realset2.html#V3">trivial</a>  <a href="struct_0.html#L1">1-sorted</a> 
 <b>by </b><i>, , <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


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