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<b>let </b><font color="Maroon">L1</font> be   <a href="lattices.html#NM7">C_Lattice</a>, <font color="Maroon">L2</font> be   <a href="lattices.html#NM7">C_Lattice</a>;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green">E14</font></i>: 
 <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> #)
 ;<br/>

<b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>, <font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>, <font color="Maroon">b2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/>



<b>assume </b><a NAME="E2:10"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> )
 ;<br/>

<b>assume </b><a NAME="E3:10"/>
<font color="Maroon">a1</font> <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E4:10"/><b>then </b><i><font color="Green">E16</font></i>: 
( <font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L1</font> &amp; <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L1</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#D18">LATTICES:def 18</a></i>;<br/>
<a NAME="E5:10"/>
( <font color="Maroon">a2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b1</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:10"/>
( <font color="Maroon">a2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L2</font> &amp; <font color="Maroon">b2</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L2</font> &amp; <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L2</font> &amp; <font color="Maroon">b2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L2</font> )
 <b>by </b><i>, <a class="ref" href="filter_2.html#T1" target="_self">Th1</a>, , </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D18">LATTICES:def 18</a><br/>


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