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<a NAME="E1:86_1_1"/>
<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/>
<a NAME="E2:86_1_1"/><b>then </b>
(  <a href="monoid_1.html#K22" target="_self">bool</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <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>) <a href="monoid_1.html#K21" target="_self">.:^2</a> </span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><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><a href="domain_1.html#K6">}</a></span> #) &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><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><a href="domain_1.html#K6">}</a></span> <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>) <a href="monoid_1.html#K21" target="_self">.:^2</a>  )
 
<b>by </b><i><a class="ref" href="monoid_1.html#D9" target="_self">Def9</a>, <a class="ref" href="monoid_1.html#T54" target="_self">Th54</a></i>;<br/>
<b>hence </b><a NAME="E3:86_1_1"/>
 <a href="monoid_1.html#K22" target="_self">bool</a> <font color="Maroon">c<sub>1</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="vectsp_1.html#L1">multLoopStr</a> 
 <b>by </b><i><a class="ref" href="monoid_0.html#D21">MONOID_0:def 21</a></i>;<br/>


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