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<a NAME="E1:86_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>) <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a> 
 
<b>by </b><i><a class="ref" href="monoid_0.html#D10" title="MONOID_0:def.10">MONOID_0:def 10</a></i>;<br/>
<a NAME="E2:86_1_1"/><b>then </b>
(  <a href="monoid_1.html#K22" title="MONOID_1:func.22">bool</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>) <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a> </span>)</span>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> #) &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>) <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a>  )
 
<b>by </b><i><a class="ref" href="monoid_1.html#D9" target="_self" title="MONOID_1:def.9">Def9</a>, <a class="ref" href="monoid_1.html#T54" target="_self" title="MONOID_1:th.54">Th54</a></i>;<br/>
<b>hence </b><a NAME="E3:86_1_1"/>
 <a href="monoid_1.html#K22" title="MONOID_1:func.22">bool</a> <font color="Maroon" title="c1">G</font> is  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="vectsp_1.html#V1" title="VECTSP_1:attr.1">strict</a> <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">well-unital</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a> 
 <b>by </b><i><a class="ref" href="monoid_0.html#D21" title="MONOID_0:def.21">MONOID_0:def 21</a></i>;<br/>


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