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<div><div><a NAME="S18"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: NAT_1:sch 18</font></span><br/></a><span class="lab"><font color="Green" title="E18">MinPred</font></span>{ <font color="Maroon">F<sub>1</sub></font>(  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>) <span class="kw">-&gt; </span>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] } :<br/><div class="add"><a NAME="E2:92"/>
 ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] &amp; (  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">n</font>] holds <br/><font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> ) )
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:92"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  holds <br/>( <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) or <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] )
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