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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> or 0 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">i</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><b>suppose </b></a><a NAME="E1:26_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 ;<br/><div class="add"><a NAME="E2:26_1_1"/><b>then </b>
<font color="Maroon">i</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><b>hence </b><a NAME="E3:26_1_1"/>
 <a href="polynom8.html#K3" target="_self">pow</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2"><b>suppose </b></a><a NAME="E1:26_1_2"/><i><font color="Green">E31</font></i>: 
0 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">i</font>
 ;<br/><div class="add"><a NAME="E2:26_1_2"/><i><font color="Green">E38</font></i>: 
 <a href="polynom8.html#K3" target="_self">pow</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/><i><font color="Green">E39</font></i>:  <a href="polynom8.html#K3" target="_self">pow</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>,<font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">L</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> 
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span> <a href="vectsp_1.html#K4">"</a> 
<b>by </b><i>, </i>
;<br/><a NAME="E4:26_1_2"/><i><font color="Green">E42</font></i>: 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/><a NAME="E5:26_1_2"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>;<br/><b>hence </b><a NAME="E6:26_1_2"/>
 <a href="polynom8.html#K3" target="_self">pow</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 <b>by </b><i>, , <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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