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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: KNASTER:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="quantal1.html#V14" title="QUANTAL1:attr.14">monotone</a>  <a href="struct_0.html#NM14" title="STRUCT_0:NM.14">UnOp</a> of <font color="Olive" title="b1">L</font> holds <br/> (  <a href="knaster.html#K9" title="KNASTER:func.9">lfp</a> <font color="Olive" title="b2">f</font> <a href="abian.html#R2" title="ABIAN:pred.2">is_a_fixpoint_of</a> <font color="Olive" title="b2">f</font> &amp;  ex <font color="Olive" title="b3">O</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> st <br/>(  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b3">O</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> &amp; (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">O</font>) <a href="knaster.html#K5" title="KNASTER:func.5">+.</a> <span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="knaster.html#K9" title="KNASTER:func.9">lfp</a> <font color="Olive" title="b2">f</font> ) )</div></div>
