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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:65_1_1_1"/>
( <font color="Maroon" title="c1">G</font> is    <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a>  or  not <font color="Maroon" title="c1">G</font> is    <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1"><b>suppose </b></a><a NAME="E1:65_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> is    <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c2">L</font> = <font color="Maroon" title="c1">G</font> as    <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a>  ;<br/><a NAME="E3:65_1_1_1_1"/>
for <font color="Olive" title="b1">N</font> being   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a>   st <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font> holds <br/>the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">multLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">L</font>,the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <font color="Maroon" title="c2">L</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <font color="Olive" title="b1">N</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c3">M</font> =  <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">multLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">L</font>,the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <font color="Maroon" title="c2">L</font> #) as    <a href="monoid_0.html#M3" title="MONOID_0:mode.3">MonoidalSubStr</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="monoid_0.html#D24" target="_self" title="MONOID_0:def.24">Def24</a></i>;<br/><b>take </b>
<font color="Maroon" title="c3">M</font>
;<br/><b>thus </b><a NAME="E5:65_1_1_1_1"/>
<font color="Maroon" title="c3">M</font> is <a href="vectsp_1.html#V1" title="VECTSP_1:attr.1">strict</a>
 ;<br/><a NAME="E6:65_1_1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 ;<br/><b>hence </b><a NAME="E7:65_1_1_1_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">M</font> 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="65_1_1_1_2"><b>suppose </b></a><a NAME="E1:65_1_1_1_2"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is  not    <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c2">M</font> being  <a href="vectsp_1.html#V1" title="VECTSP_1:attr.1">strict</a>  <a href="monoid_0.html#M1" title="MONOID_0:mode.1">MonoidalExtension</a> of <font color="Maroon" title="c1">G</font>;<br/><a NAME="E3:65_1_1_1_2"/><i><font color="Green" title="E34">A2</font></i>: 
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">M</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">M</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> #)
 <b>by </b><i><a class="ref" href="monoid_0.html#D22" target="_self" title="MONOID_0:def.22">Def22</a></i>;<br/><a NAME="E4:65_1_1_1_2"/>
for <font color="Olive" title="b1">N</font> being   <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a>   st <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font> holds <br/>the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <font color="Olive" title="b1">N</font>
 <b>by </b><i><a class="txt" href="monoid_0.html#E1:65_1_1_1_2"><i><font color="Green" title="E33">A1</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c3">M</font> = <font color="Maroon" title="c2">M</font> as    <a href="monoid_0.html#M3" title="MONOID_0:mode.3">MonoidalSubStr</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="monoid_0.html#E3:65_1_1_1_2"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="monoid_0.html#D24" target="_self" title="MONOID_0:def.24">Def24</a></i>;<br/><b>take </b>
<font color="Maroon" title="c3">M</font>
;<br/><b>thus </b><a NAME="E6:65_1_1_1_2"/>
( <font color="Maroon" title="c3">M</font> is <a href="vectsp_1.html#V1" title="VECTSP_1:attr.1">strict</a> &amp; not <font color="Maroon" title="c3">M</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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