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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">c2</font>, <font color="Olive" title="b7">d1</font>, <font color="Olive" title="b8">d2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Olive" title="b5">c1</font>,<font color="Olive" title="b7">d1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Olive" title="b6">c2</font>,<font color="Olive" title="b8">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b6">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b4">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b8">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b6">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b4">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b7">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b8">d2</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">c1</font>, <font color="Maroon" title="c7">c2</font>, <font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">d2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c7">c2</font>,<font color="Maroon" title="c9">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c10">A</font> = <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">B</font> = <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c7">c2</font>,<font color="Maroon" title="c9">d2</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">D</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E4:31"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E5:31"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E14">A2</font></span>: <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c8">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<span class="lab"><font color="Green" title="E15">A3</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>
;<br/>
<a NAME="E8:31"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c6">c1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E10:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A4</font></span>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:31"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E6:31"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/>
<a NAME="E11:31"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E17">A5</font></span>: <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c4">b1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<span class="lab"><font color="Green" title="E18">A6</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>
;<br/>
<a NAME="E14:31"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c2">a1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E16:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A7</font></span>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:31"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E12:31"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/>
<span class="lab"><font color="Green" title="E20">A8</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>
;<br/>
<span class="lab"><font color="Green" title="E21">A9</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">C</font> = <font color="Maroon" title="c10">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c11">B</font> as   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E20:31"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E21:31"/>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c11">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E22:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A11</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c13">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>;<br/>
<a NAME="E23:31"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E24:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A12</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">C</font> = <font color="Maroon" title="c13">C</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:31"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="matrix_2.html#T7" title="MATRIX_2:th.7">MATRIX_2:7</a></span>;<br/>
<a NAME="E26:31"/><span class="lab"><font color="Green" title="E25">A13</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c11">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E27:31"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E26">A14</font></span>: <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E26:31"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c9">d2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E29:31"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E26:31"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c5">b2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E31:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A15</font></span>: 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:31"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E28:31"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/>
<a NAME="E32:31"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E28">A16</font></span>: <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E26:31"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c7">c2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E34:31"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E26:31"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c3">a2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/>
<a NAME="E36:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A17</font></span>: 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:31"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E33:31"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>;<br/>
<a NAME="E37:31"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E38:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A18</font></span>: 
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c14">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:31"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E22:31"><span class="lab"><font color="Green" title="E23">A11</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_13"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">i</font>, <font color="Maroon" title="c16">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c14">C</font> implies <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font> )</span><br/><span class="kw">assume </span><a NAME="E1:31_13"/><span class="lab"><font color="Green" title="E31">A19</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c14">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font></span><br/><a NAME="E2:31_13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A20</font></span>: 
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:31"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_13_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_13_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:31_13_1_1"/>
( ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31_13"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_13_1_1_1"><span class="kw">case </span></a><a NAME="E1:31_13_1_1_1"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1</span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1 = 
<span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E16:31"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E36:31"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E1:31_13"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></span>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_13_1_1_2"><span class="kw">case </span></a><a NAME="E1:31_13_1_1_2"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2</span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2 = 
<span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E16:31"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E31:31"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E1:31_13"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></span>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_13_1_1_3"><span class="kw">case </span></a><a NAME="E1:31_13_1_1_3"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1</span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1 = 
<span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:31"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E36:31"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E1:31_13"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></span>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_13_1_1_4"><span class="kw">case </span></a><a NAME="E1:31_13_1_1_4"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2</span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2 = 
<span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E20:31"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:31"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E31:31"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E1:31_13"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></span>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:31_13"/>
<font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E40:31"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c7">c2</font>,<font color="Maroon" title="c9">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T28" title="MATRIX_1:th.28">MATRIX_1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
