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<b>let </b><font color="Maroon" title="c1">f</font> be  <a href="pencil_1.html#V11" title="PENCIL_1:attr.11">TopStruct-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<b>assume </b><a NAME="E1:31_3_1"/><i><font color="Green" title="E26">A3</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="pencil_1.html#V15" title="PENCIL_1:attr.15">PLS-yielding</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D18" target="_self" title="PENCIL_1:def.18">PENCIL_1:def 18</a><br/>

<b>assume </b><a NAME="E2:31_3_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">S1</font> = <font color="Maroon" title="c2">x</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> <a href="pencil_1.html#V5" title="PENCIL_1:attr.5">with_non_trivial_blocks</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  <b>by </b><i><a class="txt" href="pencil_1.html#E1:31_3_1"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="pencil_1.html#D19" target="_self" title="PENCIL_1:def.19">Def19</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:31_3_1"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">S1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">s</font> as   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <font color="Maroon" title="c3">S1</font> <b>by </b><i><a class="txt" href="pencil_1.html#E5:31_3_1"><i><font color="Green" title="E27">A4</font></i></a></i>;<br/>
<a NAME="E7:31_3_1"/>
2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c5">s</font>
 
<b>by </b><i><a class="ref" href="pencil_1.html#D6" target="_self" title="PENCIL_1:def.6">Def6</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:31_3_1"/><i><font color="Green" title="E28">A5</font></i>: 
( <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c7">s2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">s2</font> )
 <b>by </b><i><a class="ref" href="pencil_1.html#T2" target="_self" title="PENCIL_1:th.2">Th2</a></i>;<br/>
<b>thus </b><a NAME="E10:31_3_1"/>
<font color="Maroon" title="c2">x</font> is  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> 
 <b>by </b><i><a class="txt" href="pencil_1.html#E5:31_3_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="pencil_1.html#E9:31_3_1"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>


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