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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_1"/>
( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> or  not <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a>
 ;<br/><div class="add"><a NAME="E2:29_1_1_1_1"/><b>then </b>
 <a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">A</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="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,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="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="monoid_1.html#K5" title="MONOID_1:func.5">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> #)
 <b>by </b><i><a class="ref" href="monoid_1.html#D3" target="_self" title="MONOID_1:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E3:29_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#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">A</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="29_1_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_1_2"/>
not <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a>
 ;<br/><div class="add"><a NAME="E2:29_1_1_1_2"/><b>then </b>
 <a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">A</font>,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="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c2">A</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="monoid_1.html#D3" target="_self" title="MONOID_1:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E3:29_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#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">A</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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