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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L1">multLoopStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:35"/><i><font color="Green">E24</font></i>: 
( ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">a</font> <a href="group_1.html#K1">*</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> <font color="Olive">a</font> ) &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <span class="p1">(<span class="default"><font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font></span>)</span> ) )
 ;<br/>

<b>assume </b><a NAME="E2:35"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:35"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</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="txt" href="algstr_1.html#E13"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="txt" href="algstr_1.html#E13"><i><font color="Green">Lemma32</font></i></a>, <a class="txt" href="algstr_1.html#E15"><i><font color="Green">Lemma34</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="algstr_1.html#E13"><i><font color="Green">Lemma32</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="algstr_1.html#E13"><i><font color="Green">Lemma32</font></i></a>, <a class="txt" href="algstr_1.html#E14"><i><font color="Green">Lemma33</font></i></a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="txt" href="algstr_1.html#E13"><i><font color="Green">Lemma32</font></i></a>, <a class="txt" href="algstr_1.html#E15"><i><font color="Green">Lemma34</font></i></a></i>
;<br/>


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