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<div class="add">

<a NAME="E1:23_1_1"/>
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="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:23_1_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G2" title="ALGSTR_0:aggr.2">addLoopStr</a>(# <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="prvect_1.html#K2" title="PRVECT_1:func.2">product</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">.--&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="prvect_1.html#D3" target="_self" title="PRVECT_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E2:23_1_1_1"/>
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="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c3">d</font> = <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-Mult_over</a> <font color="Maroon" title="c1">F</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,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="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font></span>)</span> ;<br/>
<b>set </b><font color="Maroon" title="c4">G</font> = <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>;<br/>
<b>take </b>
 <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon" title="c3">d</font> #)
;<br/>

<b>thus </b><a NAME="E3:23_1_1"/>
(  <a href="algstr_0.html#G2" title="ALGSTR_0:aggr.2">addLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon" title="c3">d</font> #),the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon" title="c3">d</font> #),the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon" title="c3">d</font> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font> &amp; the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">VectSpStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K5" title="PRVECT_1:func.5">-Group_over</a> <font color="Maroon" title="c1">F</font>),<font color="Maroon" title="c3">d</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K6" title="PRVECT_1:func.6">-Mult_over</a> <font color="Maroon" title="c1">F</font> )
 ;<br/>


</div>
