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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c2">g</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E2:135"/><i><font color="Green" title="E60">A1</font></i>: 
( <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D37" target="_self" title="MONOID_0:def.37">Def37</a>, <a class="ref" href="partfun1.html#T119" title="PARTFUN1:th.119">PARTFUN1:119</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font></span>)</span> ;<br/>
<b>set </b><font color="Maroon" title="c4">op</font> = <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font>);<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c6">j</font> = <font color="Maroon" title="c5">h</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="monoid_0.html#E2:135"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="partfun1.html#T120" title="PARTFUN1:th.120">PARTFUN1:120</a></i>;<br/><b>thus </b><font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font>) <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">h</font> = 
<font color="Maroon" title="c3">f</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c5">h</font>

<br/>.= 
<font color="Maroon" title="c2">g</font> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="ref" href="monoid_0.html#D37" target="_self" title="MONOID_0:def.37">Def37</a></i>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="ref" href="partfun1.html#T37" title="PARTFUN1:th.37">PARTFUN1:37</a></i>
;<br/><b>thus </b><font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font>) <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c5">h</font>,<font color="Maroon" title="c3">f</font> = 
<font color="Maroon" title="c5">h</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c3">f</font>

<br/>.= 
<font color="Maroon" title="c6">j</font> <a href="monoid_0.html#NK2" title="MONOID_0:NK.2">(*)</a> <font color="Maroon" title="c2">g</font>
<b>by </b><i><a class="ref" href="monoid_0.html#D37" target="_self" title="MONOID_0:def.37">Def37</a></i>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="ref" href="partfun1.html#T36" title="PARTFUN1:th.36">PARTFUN1:36</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:135"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font>)
 
<b>by </b><i><a class="ref" href="binop_1.html#T11" title="BINOP_1:th.11">BINOP_1:11</a></i>;<br/>
<b>hence </b><a NAME="E6:135"/>
 <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K12" title="MONOID_0:func.12">GPFuncs</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a></i>;<br/>


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