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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</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 <font color="Maroon" title="c1">L</font>;<br/>



<a NAME="E1:50"/>
 ex <font color="Olive" title="b1">P</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="knaster.html#V2" title="KNASTER:attr.2">with_suprema</a> <a href="knaster.html#V3" title="KNASTER:attr.3">with_infima</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">x</font> where <font color="Olive" title="b2">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> : <font color="Olive" title="b2">x</font> <a href="abian.html#R2" title="ABIAN:pred.2">is_a_fixpoint_of</a> <font color="Maroon" title="c2">f</font> </span>}</span>  &amp;  <a href="knaster.html#K8" title="KNASTER:func.8">FixPoints</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="knaster.html#K7" title="KNASTER:func.7">latt</a> <font color="Olive" title="b1">P</font> )
 
<b>by </b><i><a class="ref" href="knaster.html#D11" target="_self" title="KNASTER:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E2:50"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="knaster.html#K8" title="KNASTER:func.8">FixPoints</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> : <font color="Olive" title="b1">x</font> <a href="abian.html#R2" title="ABIAN:pred.2">is_a_fixpoint_of</a> <font color="Maroon" title="c2">f</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="knaster.html#D10" target="_self" title="KNASTER:def.10">Def10</a></i>;<br/>


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