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<span class="kw">let </span><font color="Maroon" title="c1">a11</font>, <font color="Maroon" title="c2">a12</font>, <font color="Maroon" title="c3">a13</font>, <font color="Maroon" title="c4">a21</font>, <font color="Maroon" title="c5">a22</font>, <font color="Maroon" title="c6">a23</font>, <font color="Maroon" title="c7">a31</font>, <font color="Maroon" title="c8">a32</font>, <font color="Maroon" title="c9">a33</font>, <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">b2</font>, <font color="Maroon" title="c12">b3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a><br/>  for <font color="Olive" title="b2">B</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,1,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">a11</font>,<font color="Maroon" title="c2">a12</font>,<font color="Maroon" title="c3">a13</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">a21</font>,<font color="Maroon" title="c5">a22</font>,<font color="Maroon" title="c6">a23</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c7">a31</font>,<font color="Maroon" title="c8">a32</font>,<font color="Maroon" title="c9">a33</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c11">b2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c12">b3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> holds <br/><font color="Olive" title="b1">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c13">A</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B</font> being   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,1,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Maroon" title="c13">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">a11</font>,<font color="Maroon" title="c2">a12</font>,<font color="Maroon" title="c3">a13</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">a21</font>,<font color="Maroon" title="c5">a22</font>,<font color="Maroon" title="c6">a23</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c7">a31</font>,<font color="Maroon" title="c8">a32</font>,<font color="Maroon" title="c9">a33</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> &amp; <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c11">b2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c12">b3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> holds <br/><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c14">B</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,1,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">a11</font>,<font color="Maroon" title="c2">a12</font>,<font color="Maroon" title="c3">a13</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">a21</font>,<font color="Maroon" title="c5">a22</font>,<font color="Maroon" title="c6">a23</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c7">a31</font>,<font color="Maroon" title="c8">a32</font>,<font color="Maroon" title="c9">a33</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> &amp; <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c11">b2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c12">b3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> implies <font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:7"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c13">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">a11</font>,<font color="Maroon" title="c2">a12</font>,<font color="Maroon" title="c3">a13</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">a21</font>,<font color="Maroon" title="c5">a22</font>,<font color="Maroon" title="c6">a23</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c7">a31</font>,<font color="Maroon" title="c8">a32</font>,<font color="Maroon" title="c9">a33</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E2:7"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c11">b2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c12">b3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><br/>

<a NAME="E3:7"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
(  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c13">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T23" onmouseover="rs('matrix_0/T23')" onmouseout="rh()">MATRIX_0:23</a></span>;<br/>
<a NAME="E4:7"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp;  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="matrix_3.html#D4" onmouseover="rs('matrix_3/D4')" onmouseout="rh()">MATRIX_3:def 4</a></span>;<br/>
<a NAME="E5:7"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
<font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font> is   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of 3,1,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="ref" href="matrix_0.html#T20" onmouseover="rs('matrix_0/T20')" onmouseout="rh()">MATRIX_0:20</a></span>;<br/>
<a NAME="E6:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A6</font></span>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T2" onmouseover="rs('anproj_8/T2')" onmouseout="rh()">ANPROJ_8:2</a>, <a class="ref" href="matrix_0.html#T23" onmouseover="rs('matrix_0/T23')" onmouseout="rh()">MATRIX_0:23</a></span>;<br/>
<a NAME="E7:7"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
(  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">a11</font>,<font color="Maroon" title="c2">a12</font>,<font color="Maroon" title="c3">a13</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp;  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c4">a21</font>,<font color="Maroon" title="c5">a22</font>,<font color="Maroon" title="c6">a23</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp;  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,3) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c7">a31</font>,<font color="Maroon" title="c8">a32</font>,<font color="Maroon" title="c9">a33</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="anproj_9.html#T4" target="_self" onmouseover="rs('anproj_9/T4')" onmouseout="rh()">Th05</a></span>;<br/>
<a NAME="E8:7"/>
( 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; 3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/>
<a NAME="E9:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A8</font></span>: 
( 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">B</font> &amp; 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">B</font> &amp; 3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a>, <a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font> &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font> &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b3</font> )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:7_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="matrix_0.html#D8" onmouseover="rs('matrix_0/D8')" onmouseout="rh()">MATRIX_0:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font> &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font> &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b3</font> )</span><br/><a NAME="E2:7_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c14">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T23" onmouseover="rs('matrix_0/T23')" onmouseout="rh()">MATRIX_0:23</a>, <a class="ref" href="anproj_8.html#T2" onmouseover="rs('anproj_8/T2')" onmouseout="rh()">ANPROJ_8:2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">p</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><span class="kw"> such that </span><br/><a NAME="E4:7_1"/><span class="lab"><font color="Green" title="E16">A9</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">and </span><br/><a NAME="E5:7_1"/><span class="lab"><font color="Green" title="E17">A10</font></span>: 
<font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D5" onmouseover="rs('matrix_0/D5')" onmouseout="rh()">MATRIX_0:def 5</a></span>;<br/><font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) = 
<span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7_1"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="txt" href="#E5:7_1"><span class="lab"><font color="Green" title="E17">A10</font></span></a>, <a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E9">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c10">b1</font>

;<br/><span class="kw">hence </span><a NAME="E7:7_1"/>
<span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:7"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="ref" href="matrix_0.html#D8" onmouseover="rs('matrix_0/D8')" onmouseout="rh()">MATRIX_0:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font> &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b3</font> )</span><br/><a NAME="E8:7_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c14">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T23" onmouseover="rs('matrix_0/T23')" onmouseout="rh()">MATRIX_0:23</a>, <a class="ref" href="anproj_8.html#T2" onmouseover="rs('anproj_8/T2')" onmouseout="rh()">ANPROJ_8:2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">p</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><span class="kw"> such that </span><br/><a NAME="E10:7_1"/><span class="lab"><font color="Green" title="E18">A11</font></span>: 
<font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <span class="kw">and </span><br/><a NAME="E11:7_1"/><span class="lab"><font color="Green" title="E19">A12</font></span>: 
<font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D5" onmouseover="rs('matrix_0/D5')" onmouseout="rh()">MATRIX_0:def 5</a></span>;<br/><font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) = 
<span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c11">b2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:7_1"><span class="lab"><font color="Green" title="E18">A11</font></span></a>, <a class="txt" href="#E11:7_1"><span class="lab"><font color="Green" title="E19">A12</font></span></a>, <a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E9">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c11">b2</font>

;<br/><span class="kw">hence </span><a NAME="E13:7_1"/>
<span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:7"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="ref" href="matrix_0.html#D8" onmouseover="rs('matrix_0/D8')" onmouseout="rh()">MATRIX_0:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b3</font></span><br/><a NAME="E14:7_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,1</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_0.html#K2" title="MATRIX_0:func.2">Indices</a> <font color="Maroon" title="c14">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T23" onmouseover="rs('matrix_0/T23')" onmouseout="rh()">MATRIX_0:23</a>, <a class="ref" href="anproj_8.html#T2" onmouseover="rs('anproj_8/T2')" onmouseout="rh()">ANPROJ_8:2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">p</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><span class="kw"> such that </span><br/><a NAME="E16:7_1"/><span class="lab"><font color="Green" title="E20">A13</font></span>: 
<font color="Maroon" title="c17">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3
 <span class="kw">and </span><br/><a NAME="E17:7_1"/><span class="lab"><font color="Green" title="E21">A14</font></span>: 
<font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D5" onmouseover="rs('matrix_0/D5')" onmouseout="rh()">MATRIX_0:def 5</a></span>;<br/><font color="Maroon" title="c14">B</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) = 
<span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c12">b3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:7_1"><span class="lab"><font color="Green" title="E20">A13</font></span></a>, <a class="txt" href="#E17:7_1"><span class="lab"><font color="Green" title="E21">A14</font></span></a>, <a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E9">A2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c12">b3</font>

;<br/><span class="kw">hence </span><a NAME="E19:7_1"/>
<span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:7"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="ref" href="matrix_0.html#D8" onmouseover="rs('matrix_0/D8')" onmouseout="rh()">MATRIX_0:def 8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A15</font></span>: 
 <a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">b2</font>,<font color="Maroon" title="c12">b3</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) <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="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) <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="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) <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="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span> )</span></a><div class="add"><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) = 
<span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,1)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E6:7"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="matrix_3.html#D4" onmouseover="rs('matrix_3/D4')" onmouseout="rh()">MATRIX_3:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E11:7"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="ref" href="anproj_8.html#T7" onmouseover="rs('anproj_8/T7')" onmouseout="rh()">ANPROJ_8:7</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) <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="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) <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="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span> )</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) = 
<span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,2)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E6:7"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="matrix_3.html#D4" onmouseover="rs('matrix_3/D4')" onmouseout="rh()">MATRIX_3:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E11:7"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="ref" href="anproj_8.html#T7" onmouseover="rs('anproj_8/T7')" onmouseout="rh()">ANPROJ_8:7</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) <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="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) = 
<span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c13">A</font>,3)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K8" title="MATRIX_0:func.8">Col</a> (<font color="Maroon" title="c14">B</font>,1)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E6:7"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="matrix_3.html#D4" onmouseover="rs('matrix_3/D4')" onmouseout="rh()">MATRIX_3:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</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">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E11:7"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="ref" href="anproj_8.html#T7" onmouseover="rs('anproj_8/T7')" onmouseout="rh()">ANPROJ_8:7</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E13:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A16</font></span>: 
(  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> &amp;  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> &amp;  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,3) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="anproj_8.html#T90" onmouseover="rs('anproj_8/T90')" onmouseout="rh()">ANPROJ_8:90</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,1) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,2) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,3) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:7_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="matrix_3.html#D4" onmouseover="rs('matrix_3/D4')" onmouseout="rh()">MATRIX_3:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,1) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,2) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,3) )</span><br/><a NAME="E2:7_3"/>
( 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; 3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" onmouseover="rs('finseq_1/T1')" onmouseout="rh()">FINSEQ_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:7_3"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,1) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,2) &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font></span>)</span>,3) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="matrix_0.html#T52" onmouseover="rs('matrix_0/T52')" onmouseout="rh()">MATRIX_0:52</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E15:7"/>
<font color="Maroon" title="c13">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c14">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a11</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a12</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">a13</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">a21</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">a22</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">a23</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">a31</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c8">a32</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">a33</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b3</font></span>)</span></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:7"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
