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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">A1</font>, <font color="Olive" title="b2">B1</font>, <font color="Olive" title="b3">A2</font>, <font color="Olive" title="b4">B2</font> being  <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font> holds  <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b1">A1</font>,<font color="Olive" title="b2">B1</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Olive" title="b3">A2</font>,<font color="Olive" title="b4">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b3">A2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">B1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b4">B2</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c2">A1</font>, <font color="Maroon" title="c3">B1</font>, <font color="Maroon" title="c4">A2</font>, <font color="Maroon" title="c5">B2</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</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"> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">A1</font>,<font color="Maroon" title="c3">B1</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A2</font>,<font color="Maroon" title="c5">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c4">A2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B2</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span><br/>









<a NAME="E1:108"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c2">A1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">A2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<b>hence </b><span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">A1</font>,<font color="Maroon" title="c3">B1</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c4">A2</font>,<font color="Maroon" title="c5">B2</font></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c2">A1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">A2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">B1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c5">B2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="matrixj1.html#T67" target="_self" title="MATRIXJ1:th.67">Th67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c2">A1</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span> <a href="matrixj1.html#K26" title="MATRIXJ1:func.26">(+)</a> <span class="p2"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">A2</font></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span></span>)</span> <a href="matrixj1.html#K3" title="MATRIXJ1:func.3">^</a> <span class="p1"><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B2</font></span>)</span></span><a href="matrixj1.html#K4" title="MATRIXJ1:func.4">*&gt;</a></span>
<b>by </b><i><a class="ref" href="matrixj1.html#T69" target="_self" title="MATRIXJ1:th.69">Th69</a></i>
<br/>.= 
<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c4">A2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c5">B2</font></span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>
<b>by </b><i><a class="ref" href="matrixj1.html#T69" target="_self" title="MATRIXJ1:th.69">Th69</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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