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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <a href="gr_cy_1.html#K3">INT.Group</a> ,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <a href="gr_cy_1.html#K3">INT.Group</a> ,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:43_1_2"/><i><font color="Green">E75</font></i>: 
for <font color="Olive">n</font> being  <a href="int_1.html#NM1">Integer</a> holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Olive">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:43_1_2"/><i><font color="Green">E78</font></i>: 
for <font color="Olive">n</font> being  <a href="int_1.html#NM1">Integer</a> holds  <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Olive">n</font></span>)</span>
 ;<br/>

<a NAME="E3:43_1_2"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3">INT.Group</a>  holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3">INT.Group</a> ;<br/>

<b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:43_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
