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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>thus </b><a NAME="E1:46"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="group_1.html#E49"><i><font color="Green">Lemma28</font></i></a></i>;<br/>

<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> 1</span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T48" target="_self">Th48</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T44" target="_self">Th44</a></i>
;<br/>


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