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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  )</span><br/>

<a NAME="E1:124"/>
 <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K9" title="MONOID_0:func.9">*+^</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D34" target="_self" onmouseover="rs('monoid_0/D34')" onmouseout="rh()">Def34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:124"/>
( <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T60" target="_self" onmouseover="rs('monoid_0/T60')" onmouseout="rh()">Th60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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