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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#V2" title="ORDERS_2:attr.2">reflexive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:19_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 ;<br/>

<b>thus </b><a NAME="E2:19_1_1"/>
<font color="Maroon" title="c1">L</font> is <a href="waybel_1.html#V2" title="WAYBEL_1:attr.2">distributive</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D3" title="WAYBEL_1:def.3">WAYBEL_1:def 3</a><br/>

<b>thus </b><a NAME="E1:19_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c4">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:19_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="realset2.html#D7" title="REALSET2:def.7">REALSET2:def 7</a></i>;<br/>


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

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D24" title="WAYBEL_1:def.24">WAYBEL_1:def 24</a><br/>

<b>take </b><font color="Maroon" title="c3">y</font> = <font color="Maroon" title="c2">x</font>;<br/>

<b>thus </b><a NAME="E3:19_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:19_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="realset2.html#D7" title="REALSET2:def.7">REALSET2:def 7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D23" title="WAYBEL_1:def.23">WAYBEL_1:def 23</a><br/>

<b>thus </b><a NAME="E4:19_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:19_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="realset2.html#D7" title="REALSET2:def.7">REALSET2:def 7</a></i>;<br/>


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