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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattices.html#V17">Boolean</a> <a href="lattices.html#NM1">Lattice</a>;<br/>

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the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
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for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E4:45"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is    <a href="lattice4.html#M3" target="_self">Field</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="lattice4.html#D14" target="_self">Def14</a></i>;<br/>


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