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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">K</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> <br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">R1</font>, <font color="Olive" title="b4">R2</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</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="Olive" title="b1">K</font> holds <br/> ( <font color="Olive" title="b2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b3">R1</font>,<font color="Olive" title="b4">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b3">R1</font></span>)</span>,<font color="Olive" title="b4">R2</font>) &amp; <font color="Olive" title="b2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b3">R1</font>,<font color="Olive" title="b4">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b3">R1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b4">R2</font></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b2">R1</font>, <font color="Olive" title="b3">R2</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</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="c2">K</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b2">R1</font>,<font color="Olive" title="b3">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b2">R1</font></span>)</span>,<font color="Olive" title="b3">R2</font>) &amp; <font color="Olive" title="b1">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b2">R1</font>,<font color="Olive" title="b3">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b2">R1</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b3">R2</font></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font>; <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">R1</font>, <font color="Olive" title="b2">R2</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</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="c2">K</font> holds <br/> ( <font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b1">R1</font>,<font color="Olive" title="b2">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b1">R1</font></span>)</span>,<font color="Olive" title="b2">R2</font>) &amp; <font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b1">R1</font>,<font color="Olive" title="b2">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Olive" title="b1">R1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Olive" title="b2">R2</font></span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">R1</font>, <font color="Maroon" title="c5">R2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</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="c2">K</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="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<font color="Maroon" title="c5">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c4">R1</font></span>)</span>,<font color="Maroon" title="c5">R2</font>) &amp; <font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<font color="Maroon" title="c5">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R2</font></span>)</span>) )</span><br/>









<span class="kw">thus </span><a NAME="E1:78"/>
<font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<font color="Maroon" title="c5">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c4">R1</font></span>)</span>,<font color="Maroon" title="c5">R2</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseqop.html#T26" title="FINSEQOP:th.26">FINSEQOP:26</a></span>; <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="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<font color="Maroon" title="c5">R2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R2</font></span>)</span>)</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<font color="Maroon" title="c5">R2</font>)</span>)</span> = 
<font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c5">R2</font>,<font color="Maroon" title="c4">R1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseqop.html#T33" title="FINSEQOP:th.33">FINSEQOP:33</a></span>
<br/>.= 
 <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R2</font></span>)</span>,<font color="Maroon" title="c4">R1</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseqop.html#T26" title="FINSEQOP:th.26">FINSEQOP:26</a></span>
<br/>.= 
 <a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> (<font color="Maroon" title="c4">R1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c5">R2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseqop.html#T33" title="FINSEQOP:th.33">FINSEQOP:33</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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