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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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp; the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> </span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  &amp;  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</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>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">M</font> = <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> ;<br/>
<a NAME="E1:134"/>
(  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> </span>)</span>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</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>  &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> ) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D22" target="_self" title="MONOID_0:def.22">Def22</a>, <a class="ref" href="monoid_0.html#T19" target="_self" title="MONOID_0:th.19">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:134"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp; the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</a> </span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a>  &amp;  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K10" title="MONOID_0:func.10">*+^+&lt;0&gt;</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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D34" target="_self" title="MONOID_0:def.34">Def34</a>, <a class="ref" href="monoid_0.html#T69" target="_self" title="MONOID_0:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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