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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>reconsider </b><font color="Maroon">g</font> =  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font> as   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>,<font color="Maroon">X</font> ;<br/>
<a NAME="E2:139"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">X</font>,<font color="Maroon">X</font> &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font>) <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">X</font>,<font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T16" target="_self">Th16</a>, <a class="ref" href="partfun1.html#T119">PARTFUN1:119</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font></span>)</span> ;<br/>
<b>set </b><font color="Maroon">op</font> = <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font>);<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="139_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">j</font> = <font color="Maroon">h</font> as   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>,<font color="Maroon">X</font> <b>by </b><i>, <a class="ref" href="partfun1.html#T120">PARTFUN1:120</a></i>;<br/><b>thus </b><font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">f</font>,<font color="Maroon">h</font> = 
<font color="Maroon">f</font> <a href="monoid_0.html#K2" target="_self">[*]</a> <font color="Maroon">h</font>

<br/>.= 
<font color="Maroon">g</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T16" target="_self">Th16</a></i>
<br/>.= 
<font color="Maroon">h</font>
<b>by </b><i><a class="ref" href="partfun1.html#T37">PARTFUN1:37</a></i>
;<br/><b>thus </b><font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font>) <a href="binop_1.html#K2">.</a> <font color="Maroon">h</font>,<font color="Maroon">f</font> = 
<font color="Maroon">h</font> <a href="monoid_0.html#K2" target="_self">[*]</a> <font color="Maroon">f</font>

<br/>.= 
<font color="Maroon">j</font> <a href="monoid_0.html#NK2" target="_self">(*)</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T16" target="_self">Th16</a></i>
<br/>.= 
<font color="Maroon">h</font>
<b>by </b><i><a class="ref" href="partfun1.html#T36">PARTFUN1:36</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:139"/><b>then </b>
<font color="Maroon">f</font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font>)
 
<b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E6:139"/>
 <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K13" target="_self">GPFuncs</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>


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