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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:85_1_1_1"/>
( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> or  not <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1_1"><b>suppose </b></a><a NAME="E1:85_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>
 ;<br/><div class="add"><a NAME="E2:85_1_1_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="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default">the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <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> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> #)
 <b>by </b><i><a class="ref" href="monoid_1.html#D9" target="_self" title="MONOID_1:def.9">Def9</a></i>;<br/><b>hence </b><a NAME="E3:85_1_1_1_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K22" title="MONOID_1:func.22">bool</a> <font color="Maroon" title="c1">G</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_1_2"><b>suppose </b></a><a NAME="E1:85_1_1_1_2"/>
not <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>
 ;<br/><div class="add"><a NAME="E2:85_1_1_1_2"/><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="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span>,<span class="p1">(<span class="default">the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a> </span>)</span> #)
 <b>by </b><i><a class="ref" href="monoid_1.html#D9" target="_self" title="MONOID_1:def.9">Def9</a></i>;<br/><b>hence </b><a NAME="E3:85_1_1_1_2"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K22" title="MONOID_1:func.22">bool</a> <font color="Maroon" title="c1">G</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a><br/></div><b>end;</b></div></div><b>end;</b></div>

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