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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be  <a href="quantal1.html#V14">monotone</a> <a href="quantal1.html#NM1">UnOp</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">A</font></span>)</span>;<br/>



<a NAME="E1:62"/>
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">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as  <a href="cohsp_1.html#V6">V169</a> <a href="funct_2.html#NM1">Function</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">g</font>
;<br/>

<b>reconsider </b><font color="Maroon">lf</font> =  <a href="knaster.html#K9" target="_self">lfp</a> <font color="Maroon">f</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font> <b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<a NAME="E4:62"/>
 <a href="knaster.html#K9" target="_self">lfp</a> <font color="Maroon">f</font> <a href="abian.html#R2">is_a_fixpoint_of</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="knaster.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E5:62"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="knaster.html#K1" target="_self">lfp</a> <font color="Maroon">A</font>,<font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">lf</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">lg</font> =  <a href="knaster.html#K1" target="_self">lfp</a> <font color="Maroon">A</font>,<font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1">BooleLatt</a> <font color="Maroon">A</font></span>)</span> <b>by </b><i><a class="ref" href="lattice3.html#D1">LATTICE3:def 1</a></i>;<br/>
<a NAME="E7:62"/>
<font color="Maroon">lg</font> <a href="abian.html#R2">is_a_fixpoint_of</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:62"/><b>then </b>
 <a href="knaster.html#K9" target="_self">lfp</a> <font color="Maroon">f</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">lg</font>
 
<b>by </b><i><a class="ref" href="knaster.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E9:62"/><b>then </b>
<font color="Maroon">lf</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">lg</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#T2">LATTICE3:2</a></i>;<br/>
<b>hence </b><a NAME="E10:62"/>
 <a href="knaster.html#K1" target="_self">lfp</a> <font color="Maroon">A</font>,<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="knaster.html#K9" target="_self">lfp</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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