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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="lattices.html#L2" title="LATTICES:struct.2">\/-SemiLattStr</a> ;<br/>

<b>assume </b><a NAME="E1:46_1_1"/><i><font color="Green" title="E38">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="E2:46_1_1"/>
<font color="Maroon" title="c1">L</font> is <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_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> 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="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a><br/>

<b>thus </b><a NAME="E1:46_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:46_1_1"><i><font color="Green" title="E38">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>, <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="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a><br/>

<b>thus </b><a NAME="E3:46_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</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="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">z</font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:46_1_1"><i><font color="Green" title="E38">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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