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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V4">complete</a> <a href="lattices.html#NM1">Lattice</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 <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:60"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 ;<br/>

<b>then consider </b><font color="Maroon">O</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E3:60"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">O</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E4:60"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">O</font> <a href="knaster.html#K5" target="_self">+.</a> <font color="Maroon">a</font> <a href="abian.html#R2">is_a_fixpoint_of</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:60"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">f</font>,<font color="Maroon">O</font> <a href="knaster.html#K5" target="_self">+.</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:60"/>
<font color="Maroon">f</font>,<font color="Maroon">O</font> <a href="knaster.html#K5" target="_self">+.</a> <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a>  <a href="knaster.html#K10" target="_self">gfp</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="knaster.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<font color="Maroon">a</font> <a href="lattices.html#R3">[=</a>  <a href="knaster.html#K10" target="_self">gfp</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>


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