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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" 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> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font> holds  <font color="Olive" title="b1">F</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">G</font> =  <a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">F9</font> = <font color="Maroon" title="c2">F</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T73" title="MONOID_0:th.73">MONOID_0:73</a></span>;<br/>
<a NAME="E2:26"/>
<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">F9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span>
 
;<br/>
<span class="kw">then </span> <a href="group_4.html#K3" title="GROUP_4:func.3">Product</a> <span class="p1">(<span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c4">F9</font></span>)</span> = 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T8" title="GROUP_4:th.8">GROUP_4:8</a></span>
<br/>.= 
 <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#T22" title="GROUP_1:th.22">GROUP_1:22</a></span>
<br/>.= 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T75" title="MONOID_0:th.75">MONOID_0:75</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:26"/>
<font color="Maroon" title="c2">F</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp11.html#D4" target="_self" title="VECTSP11:def.4">Def4</a></span>; <a class="txt" 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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