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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be  <a href="quantal1.html#V14" title="QUANTAL1:attr.14">monotone</a> <a href="quantal1.html#NM1" title="QUANTAL1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/>



<a NAME="E1:63"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D1" title="LATTICE3:def.1">LATTICE3:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">g</font> = <font color="Maroon" title="c2">f</font> as  <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">V170</a> <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">A</font>, <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="knaster.html#T49" target="_self" title="KNASTER:th.49">Th49</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">g</font>
;<br/>

<b>reconsider </b><font color="Maroon" title="c4">gf</font> =  <a href="knaster.html#K10" title="KNASTER:func.10">gfp</a> <font color="Maroon" title="c2">f</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="lattice3.html#D1" title="LATTICE3:def.1">LATTICE3:def 1</a></i>;<br/>
<a NAME="E4:63"/>
 <a href="knaster.html#K10" title="KNASTER:func.10">gfp</a> <font color="Maroon" title="c2">f</font> <a href="abian.html#R2" title="ABIAN:pred.2">is_a_fixpoint_of</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="knaster.html#T45" target="_self" title="KNASTER:th.45">Th45</a></i>;<br/>
<a NAME="E5:63"/><b>then </b><i><font color="Green" title="E48">A1</font></i>: 
<font color="Maroon" title="c4">gf</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="knaster.html#K2" title="KNASTER:func.2">gfp</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">g</font>
 
<b>by </b><i><a class="ref" href="knaster.html#T10" target="_self" title="KNASTER:th.10">Th10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">gg</font> =  <a href="knaster.html#K2" title="KNASTER:func.2">gfp</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" title="LATTICE3:func.1">BooleLatt</a> <font color="Maroon" title="c1">A</font></span>)</span> <b>by </b><i><a class="ref" href="lattice3.html#D1" title="LATTICE3:def.1">LATTICE3:def 1</a></i>;<br/>
<a NAME="E7:63"/>
<font color="Maroon" title="c5">gg</font> <a href="abian.html#R2" title="ABIAN:pred.2">is_a_fixpoint_of</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="knaster.html#T7" target="_self" title="KNASTER:th.7">Th7</a></i>;<br/>
<a NAME="E8:63"/><b>then </b>
<font color="Maroon" title="c5">gg</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="knaster.html#K10" title="KNASTER:func.10">gfp</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="knaster.html#T46" target="_self" title="KNASTER:th.46">Th46</a></i>;<br/>
<a NAME="E9:63"/><b>then </b>
<font color="Maroon" title="c5">gg</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">gf</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#T2" title="LATTICE3:th.2">LATTICE3:2</a></i>;<br/>
<b>hence </b><a NAME="E10:63"/>
 <a href="knaster.html#K2" title="KNASTER:func.2">gfp</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="knaster.html#K10" title="KNASTER:func.10">gfp</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="knaster.html#E5:63"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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