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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V4">join-commutative</a> <a href="lattices.html#V5">join-associative</a> <a href="lattices.html#V9">join-absorbing</a>  <a href="lattices.html#L3">LattStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:4"/>
<font color="Maroon">a</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:4"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>
<b>assume </b><a NAME="E3:4"/>
<font color="Maroon">c</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">d</font>
 ;<br/>

<b>then </b><font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i>, <a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
;<br/>
<b>hence </b><a NAME="E5:4"/>
<font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>


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