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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</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">V1</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">M1</font>, <font color="Olive" title="b3">M2</font> being  <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">M1</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="Olive" title="b3">M2</font> holds <br/><span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Olive" title="b2">M1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Olive" title="b3">M2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">^^</a> <font color="Olive" title="b3">M2</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">V1</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <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">M1</font>, <font color="Olive" title="b2">M2</font> being  <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">M1</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="Olive" title="b2">M2</font> holds <br/><span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Olive" title="b1">M1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Olive" title="b2">M2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">M1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">^^</a> <font color="Olive" title="b2">M2</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V1</font>; <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="c3">M1</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="c4">M2</font> implies <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c3">M1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">^^</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M1</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="c4">M2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c3">M1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">^^</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span></span><br/>

 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c3">M1</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M1</font>
<b>by </b><i><a class="ref" href="matrlin.html#D8" target="_self" title="MATRLIN:def.8">Def8</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c4">M2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:47"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="matrlin.html#D8" target="_self" title="MATRLIN:def.8">Def8</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c3">M1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span> = 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#T34" target="_self" title="MATRLIN:th.34">Th34</a></i>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8" title="MATRLIN:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">^^</a> <font color="Maroon" title="c4">M2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#T33" target="_self" title="MATRLIN:th.33">Th33</a></i>
;<br/> <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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