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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">F</font> is <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a> implies <font color="Maroon" title="c1">F</font> is <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a> )</span><br/>

<b>assume </b><a NAME="E1:27_1_1"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">F</font> is <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> is <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a></span><br/>

<b>let </b><font color="Maroon" title="c2">i</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">F</font> or  not <font color="Maroon" title="c2">i</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )</span><br/>

<b>assume </b><a NAME="E2:27_1_1"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">i</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a></span><br/>

<a NAME="E3:27_1_1"/><b>then </b>
<font color="Maroon" title="c2">i</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="#E1:27_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="pencil_1.html#D17" target="_self" title="PENCIL_1:def.17">Def17</a></i>;<br/>
<b>hence </b><a NAME="E4:27_1_1"/>
not <font color="Maroon" title="c2">i</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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