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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">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  holds  <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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Olive" title="b2">g</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</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"> <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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c3">g</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">DC</font> = <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K11" title="MONOID_0:func.11">-concatenation</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">df</font> = <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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c6">dg</font> = <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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c3">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K9" title="MONOID_0:func.9">*+^</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D34" onmouseover="rs('monoid_0/D34')" onmouseout="rh()">MONOID_0:def 34</a></span>;<br/>
<span class="kw">thus </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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c3">g</font></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="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c3">g</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T67" onmouseover="rs('monoid_0/T67')" onmouseout="rh()">MONOID_0:67</a>, <a class="ref" href="finsop_1.html#T5" onmouseover="rs('finsop_1/T5')" onmouseout="rh()">FINSOP_1:5</a></span>
<br/>.= 
 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#K9" title="MONOID_0:func.9">*+^</a></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c3">g</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D36" onmouseover="rs('monoid_0/D36')" onmouseout="rh()">MONOID_0:def 36</a></span>
<br/>.= 
<font color="Maroon" title="c5">df</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">dg</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="algstr_0.html#D18" onmouseover="rs('algstr_0/D18')" onmouseout="rh()">ALGSTR_0:def 18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<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="finsop_1.html#K1" title="FINSOP_1:func.1">"**"</a> <font color="Maroon" title="c3">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D34" onmouseover="rs('monoid_0/D34')" onmouseout="rh()">MONOID_0:def 34</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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