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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span><br/>  for <font color="Olive" title="b4">pf</font>, <font color="Olive" title="b5">uf</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><br/>  for <font color="Olive" title="b6">N</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Maroon" title="c1">i</font> <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; <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">uf</font> &amp; <font color="Olive" title="b4">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> &amp; <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b2">u</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b6">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Olive" title="b5">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b6">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b4">pf</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">r</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">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">u</font>, <font color="Olive" title="b2">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</span><br/>  for <font color="Olive" title="b3">pf</font>, <font color="Olive" title="b4">uf</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><br/>  for <font color="Olive" title="b5">N</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Maroon" title="c1">i</font> <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; <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">uf</font> &amp; <font color="Olive" title="b3">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> &amp; <font color="Maroon" title="c2">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b5">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b3">pf</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</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">  for <font color="Olive" title="b1">pf</font>, <font color="Olive" title="b2">uf</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><br/>  for <font color="Olive" title="b3">N</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Maroon" title="c1">i</font> <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; <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">uf</font> &amp; <font color="Olive" title="b1">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c2">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b3">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b1">pf</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">pf</font>, <font color="Maroon" title="c6">uf</font> be   <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>; <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">N</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 3,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st <font color="Maroon" title="c1">i</font> <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; <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font> &amp; <font color="Maroon" title="c5">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c2">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b1">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c5">pf</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">N</font> be   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of 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"> ( <font color="Maroon" title="c1">i</font> <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; <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font> &amp; <font color="Maroon" title="c5">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c2">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c5">pf</font></span>)</span> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">i</font> <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">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font>
 <span class="kw">and </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c5">pf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">and </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c2">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E5:14"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">u</font>
 ; <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="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c5">pf</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">b</font> = 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">s1</font> = <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1, <font color="Maroon" title="c10">s2</font> = <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2, <font color="Maroon" title="c11">s3</font> = <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" onmouseover="rs('xreal_0/D1')" onmouseout="rh()">XREAL_0:def 1</a></span>;<br/>
<a NAME="E7:14"/>
<font color="Maroon" title="c3">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3
 
;<br/>
<a NAME="E8:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" onmouseover="rs('euclid/T22')" onmouseout="rh()">EUCLID:22</a></span>;<br/>
<span class="lab"><font color="Green" title="E21">A7</font></span>:  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">u</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="anproj_8.html#T75" onmouseover="rs('anproj_8/T75')" onmouseout="rh()">ANPROJ_8:75</a></span>
<br/>.= 
3
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="euclid_8.html#T50" onmouseover="rs('euclid_8/T50')" onmouseout="rh()">EUCLID_8:50</a></span>
;<br/>
<span class="lab"><font color="Green" title="E22">A8</font></span>:  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font> = 
3
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#T24" onmouseover="rs('matrix_0/T24')" onmouseout="rh()">MATRIX_0:24</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D6" onmouseover="rs('matrix_0/D6')" onmouseout="rh()">MATRIX_0:def 6</a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a></span>
;<br/>
<a NAME="E11:14"/>
<font color="Maroon" title="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span> 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="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="finseq_3.html#T153" onmouseover="rs('finseq_3/T153')" onmouseout="rh()">FINSEQ_3:153</a>, <a class="ref" href="anproj_8.html#T91" onmouseover="rs('anproj_8/T91')" onmouseout="rh()">ANPROJ_8:91</a></span>;<br/>
<a NAME="E12:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A9</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="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></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="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></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="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> )
 
<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">reconsider </span><font color="Maroon" title="c12">t1</font> = <font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1, <font color="Maroon" title="c13">t2</font> = <font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2, <font color="Maroon" title="c14">t3</font> = <font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" onmouseover="rs('xreal_0/D1')" onmouseout="rh()">XREAL_0:def 1</a></span>;<br/>
<a NAME="E14:14"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">N</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="c7">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 
<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/>
<div><span class="lab"><font color="Green" title="E25">A11</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_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"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,3) )</span></a><div class="add"><span class="kw">thus </span> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,1)</span>)</span> = 
 <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 7</a></span>
<br/>.= 
3
<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>
; <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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,3) )</span><br/><a NAME="E2:14_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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <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="E3:14_3"/>
( <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,3) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 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>
<div><span class="lab"><font color="Green" title="E26">A12</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_4"><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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,3) )</span></a><div class="add"><span class="kw">thus </span> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</span>)</span> = 
 <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 7</a></span>
<br/>.= 
3
<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>
; <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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,3) )</span><br/><a NAME="E2:14_4"/>
( 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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <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="E3:14_4"/>
( <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,2)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (2,3) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 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>
<div><span class="lab"><font color="Green" title="E27">A13</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_5"><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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,3) )</span></a><div class="add"><span class="kw">thus </span> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</span>)</span> = 
 <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 7</a></span>
<br/>.= 
3
<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>
; <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#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,3) )</span><br/><a NAME="E2:14_5"/>
( 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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Maroon" title="c7">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <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="E3:14_5"/>
( <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,1) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,2) &amp; <span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,3)</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="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (3,3) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_0.html#D7" onmouseover="rs('matrix_0/D7')" onmouseout="rh()">MATRIX_0:def 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="E18:14"/>
3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">uf</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="euclid_8.html#T50" onmouseover="rs('euclid_8/T50')" onmouseout="rh()">EUCLID_8:50</a></span>;<br/>
<a NAME="E19:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c6">uf</font> <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="c9">s1</font>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c11">s3</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/>
<a NAME="E20:14"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
 not  not <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ...  &amp;  not <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="finseq_1.html#T91" onmouseover="rs('finseq_1/T91')" onmouseout="rh()">FINSEQ_1:91</a></span>;<br/>
<span class="lab"><font color="Green" title="E30">A16</font></span>: <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c6">uf</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="rvsum_1.html#T49" onmouseover="rs('rvsum_1/T49')" onmouseout="rh()">RVSUM_1:49</a></span>
<br/>.= 
1 <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c6">uf</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" onmouseover="rs('xcmplx_1/T87')" onmouseout="rh()">XCMPLX_1:87</a></span>
<br/>.= 
<font color="Maroon" title="c6">uf</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T52" onmouseover="rs('rvsum_1/T52')" onmouseout="rh()">RVSUM_1:52</a></span>
;<br/>
<a NAME="E22:14"/>
<font color="Maroon" title="c6">uf</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a></span>;<br/>
<a NAME="E23:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<font color="Maroon" title="c6">uf</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" onmouseover="rs('euclid/T22')" onmouseout="rh()">EUCLID:22</a></span>;<br/>
<a NAME="E24:14"/>
<font color="Maroon" title="c4">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3
 
;<br/>
<a NAME="E25:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" onmouseover="rs('euclid/T22')" onmouseout="rh()">EUCLID:22</a></span>;<br/>
<span class="kw">then </span><span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3</span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> = 
<font color="Maroon" title="c6">uf</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="euclid_8.html#T52" onmouseover="rs('euclid_8/T52')" onmouseout="rh()">EUCLID_8:52</a></span>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3</span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="euclid_8.html#T1" onmouseover="rs('euclid_8/T1')" onmouseout="rh()">EUCLID_8:1</a></span>
;<br/>
<a NAME="E27:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A19</font></span>: 
( <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">uf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T78" onmouseover="rs('finseq_1/T78')" onmouseout="rh()">FINSEQ_1:78</a></span>;<br/>
<a NAME="E28:14"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<font color="Maroon" title="c5">pf</font> <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="c12">t1</font>,<font color="Maroon" title="c13">t2</font>,<font color="Maroon" title="c14">t3</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="#E3:14"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="euclid_8.html#T1" onmouseover="rs('euclid_8/T1')" onmouseout="rh()">EUCLID_8:1</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) = 
<span class="p1">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</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> (<span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span>,1)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E23">A9</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"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c6">uf</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T93" onmouseover="rs('anproj_8/T93')" onmouseout="rh()">ANPROJ_8:93</a></span>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,2)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,3)</span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c9">s1</font>,<font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c11">s3</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="#E20:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">s1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,2)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">s2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,3)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">s3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T7" onmouseover="rs('anproj_8/T7')" onmouseout="rh()">ANPROJ_8:7</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<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">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">t1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,2)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c13">t2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,3)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c14">t3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,2)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,3)</span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c12">t1</font>,<font color="Maroon" title="c13">t2</font>,<font color="Maroon" title="c14">t3</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T7" onmouseover="rs('anproj_8/T7')" onmouseout="rh()">ANPROJ_8:7</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c5">pf</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E30:14"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">N</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="laplace.html#K10" title="LAPLACE:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c6">uf</font></span><a href="laplace.html#K10" title="LAPLACE:func.10">*&gt;</a></span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Maroon" title="c7">N</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c5">pf</font></span>)</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>
