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<span class="kw">let </span><font color="Maroon" title="c1">k</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"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> holds   <a href="matrix15.html#K3" title="MATRIX15:func.3">ColVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c1">k</font>,1</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">  <a href="matrix15.html#K3" title="MATRIX15:func.3">ColVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">C</font> =  <a href="matrix15.html#K3" title="MATRIX15:func.3">ColVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> as   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">k</font>,1,<font color="Maroon" title="c2">K</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">Z</font> =  <a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:36_1"/><span class="lab"><font color="Green" title="E31">A1</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="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c5">i</font>, <font color="Maroon" title="c6">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="c5">i</font>,<font color="Maroon" title="c6">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="c3">C</font> implies <span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font> )</span><br/><span class="kw">assume </span><a NAME="E2:36_1"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">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="c3">C</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"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font></span><br/><a NAME="E3:36_1"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E4:36_1"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E5:36_1"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">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="c3">C</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></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>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></span>;<br/><a NAME="E6:36_1"/><span class="kw">then </span>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="matrix15.html#T26" target="_self" title="MATRIX15:th.26">Th26</a></span>;<br/><a NAME="E7:36_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1"><span class="lab"><font color="Green" title="E34">A4</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#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E8:36_1"/>
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c3">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T27" title="MATRIX_1:th.27">MATRIX_1:27</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="matrix_3.html#T3" title="MATRIX_3:th.3">MATRIX_3:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="txt" href="#E5:36_1"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="finseq_2.html#T71" title="FINSEQ_2:th.71">FINSEQ_2:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c6">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="txt" href="#E5:36_1"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E7:36_1"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="ref" href="matrix15.html#T26" target="_self" title="MATRIX15:th.26">Th26</a></span>
<br/>.= 
<font color="Maroon" title="c3">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c6">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</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>
<span class="kw">hence </span><a NAME="E3:36"/>
 <a href="matrix15.html#K3" title="MATRIX15:func.3">ColVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">k</font>,1
 <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/>


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