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<b>let </b><font color="Maroon" title="c1">e1</font>, <font color="Maroon" title="c2">e2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> holds <br/> <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">e1</font>,<font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font></span><br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> implies  <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">e1</font>,<font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font> )</span><br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E40">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">e1</font>,<font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span><br/>

<b>set </b><font color="Maroon" title="c5">l</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">Y</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">e</font> where <font color="Olive" title="b1">e</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c7">Z</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> </span>}</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">e3</font> = <font color="Maroon" title="c1">e1</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E3:44"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> &amp; <font color="Maroon" title="c2">e2</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
<b>by </b><i><a class="txt" href="matrprob.html#E1:44"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E4:44"/><b>then </b>
<font color="Maroon" title="c2">e2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">e</font> where <font color="Olive" title="b1">e</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">e4</font> = <font color="Maroon" title="c2">e2</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<a NAME="E6:44"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> &amp; <font color="Maroon" title="c3">f1</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
<b>by </b><i><a class="txt" href="matrprob.html#E1:44"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E7:44"/><b>then </b>
<font color="Maroon" title="c3">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">f3</font> = <font color="Maroon" title="c3">f1</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font></span>)</span> <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 <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
<a NAME="E9:44"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> &amp; <font color="Maroon" title="c4">f2</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
<b>by </b><i><a class="txt" href="matrprob.html#E1:44"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E10:44"/><b>then </b>
<font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">f4</font> = <font color="Maroon" title="c4">f2</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font></span>)</span> <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 <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  ;<br/>
<a NAME="E12:44"/>
 <a href="rvsum_1.html#K15" title="RVSUM_1:func.15">mlt</a> <font color="Maroon" title="c8">e3</font>,<font color="Maroon" title="c9">e4</font> <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="c10">f3</font>,<font color="Maroon" title="c11">f4</font>
 
<b>by </b><i><a class="txt" href="matrprob.html#E1:44"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="matrprob.html#T34" target="_self" title="MATRPROB:th.34">Th34</a></i>;<br/>
<b>hence </b><a NAME="E13:44"/>
 <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">e1</font>,<font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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