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<div><div><a NAME="S10"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: NAT_1:sch 10</font></span><br/></a><span class="lab"><font color="Green" title="E10">Indfrom1</font></span>{ <font color="Maroon">P<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] } :<br/><div class="add"><a NAME="E3:45"/>
 for <font color="Olive" title="b1">k</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:45"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[1]
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 for <font color="Olive" title="b1">k</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><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]
 </div></div></div>
