<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<b>assume </b><a NAME="E1:31_1_1"/><i><font color="Green" title="E26">A1</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>thus </b><a NAME="E2:31_1_1"/>
<font color="Maroon" title="c1">f</font> is <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D7" title="WAYBEL_3:def.7">WAYBEL_3:def 7</a><br/>

<b>assume </b><a NAME="E1:31_1_1_1"/>
<font color="Maroon" title="c2">S</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>hence </b><a NAME="E2:31_1_1_1"/>
not <font color="Maroon" title="c2">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 <b>by </b><i><a class="txt" href="pencil_1.html#E1:31_1_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="pencil_1.html#D19" target="_self" title="PENCIL_1:def.19">Def19</a></i>;<br/>


</div><b>end;</b></div>

<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#D13" target="_self" title="PENCIL_1:def.13">PENCIL_1:def 13</a><br/>

<b>assume </b><a NAME="E3:31_1_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>hence </b><a NAME="E4:31_1_1"/>
<font color="Maroon" title="c2">x</font> is    <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_1_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="pencil_1.html#D19" target="_self" title="PENCIL_1:def.19">Def19</a></i>;<br/>


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