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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>for <font color="Olive" title="b1">G</font> being  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> $1</span>)</span> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> $1;<br/>
<a NAME="E1:28"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="txt" href="group_3.html#E37"><i><font color="Green" title="E21">Lm3</font></i></a></i>;<br/>
<a NAME="E2:28"/><i><font color="Green" title="E25">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1]
 
<b>by </b><i><a class="txt" href="group_3.html#E38"><i><font color="Green" title="E22">Lm4</font></i></a></i>;<br/>
<a NAME="E3:28"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="group_3.html#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="group_3.html#E2:28"><i><font color="Green" title="E25">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:28"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">G</font> being  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/> for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Olive" title="b1">n</font>
 ;<br/>


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