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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:31_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="pencil_1.html#V15" target="_self">PLS-yielding</a>
 ;<br/>

<b>thus </b><a NAME="E2:31_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V4">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">c<sub>2</sub></font> be    <a href="struct_0.html#L1">1-sorted</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D7">WAYBEL_3:def 7</a><br/>

<b>assume </b><a NAME="E1:31_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:31_1_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i><a class="txt" href="pencil_1.html#E1:31_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="pencil_1.html#D19" target="_self">Def19</a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D13" target="_self">PENCIL_1:def 13</a><br/>

<b>assume </b><a NAME="E3:31_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E4:31_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="pre_topc.html#L1">TopStruct</a> 
 <b>by </b><i><a class="txt" href="pencil_1.html#E1:31_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="pencil_1.html#D19" target="_self">Def19</a></i>;<br/>


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