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<div><div><a NAME="S2"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: HALLMAR1:sch 2</font></span><br/></a><span class="lab"><font color="Green" title="E2">Regr2</font></span>{ <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] } :<br/><div class="add"><a NAME="E3:3"/>
<font color="Maroon">P<sub>1</sub></font>[1]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:3"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
 ex <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <br/>( <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] )
 <span class="kw">and </span><br/><a NAME="E2:3"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
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