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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L2">\/-SemiLattStr</a> ;<br/>

<b>assume </b><a NAME="E1:46_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>thus </b><a NAME="E2:46_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V4">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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D4">LATTICES:def 4</a><br/>

<b>thus </b><a NAME="E1:46_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:46_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a><br/>

<b>thus </b><a NAME="E3:46_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="sheffer1.html#E1:46_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


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