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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="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:49"/>
 <a href="lattice3.html#K3">LattPOSet</a> <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <span class="p2">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice3.html#D2">LATTICE3:def 2</a></i>;<br/>
<b>then </b><i><font color="Green">E23</font></i>: the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_1.html#D2">YELLOW_1:def 2</a></i>
<br/>.= 
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E3:49"/>
( <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>thus </b><a NAME="E4:49"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="waybel_8.html#E2:49"><i><font color="Green">E23</font></i></a></i>;<br/>


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