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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="lattices.html#NM8">B_Lattice</a>;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E7</font></i>: 
 <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>

<b>let </b><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>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E2:11"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7">`</a>  as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="filter_2.html#E1:11"><i><font color="Green">E7</font></i></a></i>;<br/>
<a NAME="E4:11"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7">`</a>  <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D21">LATTICES:def 21</a></i>;<br/>
<a NAME="E5:11"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="filter_2.html#E1:11"><i><font color="Green">E7</font></i></a>, <a class="txt" href="filter_2.html#E2:11"><i><font color="Green">E8</font></i></a>, <a class="ref" href="filter_2.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E6:11"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K7">`</a> 
 <b>by </b><i><a class="ref" href="lattices.html#D21">LATTICES:def 21</a></i>;<br/>


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