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<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="setwiseo.html#NR1" target="_self">has_a_unity</a> 
 
<b>by </b><i><a class="ref" href="monoid_0.html#D10">MONOID_0:def 10</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:39_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>)
 <b>by </b><i><a class="ref" href="setwiseo.html#D2">SETWISEO:def 2</a></i>;<br/>
<a NAME="E4:39_1_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp;  <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span></span>)</span> #) )
 
<b>by </b><i><a class="txt" href="monoid_1.html#E3:39_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="monoid_1.html#D3" target="_self">Def3</a>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>
<a NAME="E5:39_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="monoid_1.html#E3:39_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="monoid_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E6:39_1_1"/>
 <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is  non <a href="struct_0.html#V3">empty</a> <a href="vectsp_1.html#V1">strict</a> <a href="vectsp_2.html#V1">well-unital</a> <a href="monoid_0.html#V1">constituted-Functions</a>  <a href="vectsp_1.html#L1">multLoopStr</a> 
 <b>by </b><i><a class="txt" href="monoid_1.html#E4:39_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="monoid_0.html#D21">MONOID_0:def 21</a></i>;<br/>


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