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<b>let </b><font color="Maroon">UA</font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="endalg.html#K3" target="_self">UAEndMonoid</a> <font color="Maroon">UA</font></span>)</span>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="endalg.html#K3" target="_self">UAEndMonoid</a> <font color="Maroon">UA</font></span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="endalg.html#K1" target="_self">UAEnd</a> <font color="Maroon">UA</font>, <font color="Maroon">g</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="endalg.html#K1" target="_self">UAEnd</a> <font color="Maroon">UA</font>;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">i</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">UA</font> as    <a href="fraenkel.html#M2">Element</a> of  <a href="endalg.html#K1" target="_self">UAEnd</a> <font color="Maroon">UA</font> <b>by </b><i/>;<br/>
<a NAME="E3:10"/>
 <a href="endalg.html#K3" target="_self">UAEndMonoid</a> <font color="Maroon">UA</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="endalg.html#K1" target="_self">UAEnd</a> <font color="Maroon">UA</font></span>)</span>,<span class="p1">(<span class="default"><a href="endalg.html#K2" target="_self">UAEndComp</a> <font color="Maroon">UA</font></span>)</span>,<font color="Maroon">i</font> #)
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:10"/>
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 <b>by </b><i>, </i>;<br/>


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