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<span class="kw">let </span><font color="Maroon" title="c1">n</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="firebrick">::  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><br/>  for <font color="Olive" title="b2">L</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">V</font> being   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b4">F</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">V</font>,<font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b5">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b6">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b5">V1</font>,<font color="Olive" title="b5">V1</font>  st <font color="Olive" title="b5">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b3">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b4">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b5">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b6">F1</font> holds <br/> ex <font color="Olive" title="b7">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Olive" title="b2">L</font>,<font color="Olive" title="b1">K</font> ex <font color="Olive" title="b8">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b5">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b6">F1</font>,<font color="Olive" title="b8">b1</font>,<font color="Olive" title="b8">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b7">J</font>,<span class="p1">(<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><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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b4">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V</font><br/>  for <font color="Olive" title="b5">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b4">V1</font>,<font color="Olive" title="b4">V1</font>  st <font color="Olive" title="b4">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b3">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b4">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">F1</font> holds <br/> ex <font color="Olive" title="b6">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Olive" title="b1">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b7">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b5">F1</font>,<font color="Olive" title="b7">b1</font>,<font color="Olive" title="b7">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b6">J</font>,<span class="p1">(<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><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">V1</font>,<font color="Olive" title="b3">V1</font>  st <font color="Olive" title="b3">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b2">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b3">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">F1</font> holds <br/> ex <font color="Olive" title="b5">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b6">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b4">F1</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b6">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b5">J</font>,<span class="p1">(<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><br/><span class="kw">let </span><font color="Maroon" title="c4">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c4">V</font><br/>  for <font color="Olive" title="b2">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c4">V</font><br/>  for <font color="Olive" title="b3">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b2">V1</font>  st <font color="Olive" title="b2">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b1">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b2">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">F1</font> holds <br/> ex <font color="Olive" title="b4">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b5">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b3">F1</font>,<font color="Olive" title="b5">b1</font>,<font color="Olive" title="b5">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b4">J</font>,<span class="p1">(<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><br/><span class="kw">let </span><font color="Maroon" title="c5">F</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c4">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c4">V</font><br/>  for <font color="Olive" title="b2">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b1">V1</font>  st <font color="Olive" title="b1">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b1">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">F1</font> holds <br/> ex <font color="Olive" title="b3">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b4">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b2">F1</font>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b4">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b3">J</font>,<span class="p1">(<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><br/><span class="kw">let </span><font color="Maroon" title="c6">V1</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c4">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c6">V1</font>,<font color="Maroon" title="c6">V1</font>  st <font color="Maroon" title="c6">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c6">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">F1</font> holds <br/> ex <font color="Olive" title="b2">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b3">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c6">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b1">F1</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b3">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b2">J</font>,<span class="p1">(<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><br/><span class="kw">let </span><font color="Maroon" title="c7">F1</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c6">V1</font>,<font color="Maroon" title="c6">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c6">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c7">F1</font> implies  ex <font color="Olive" title="b1">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b2">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c6">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b2">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b1">J</font>,<span class="p1">(<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><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:52"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c6">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:52"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c6">V1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c7">F1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b2">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c6">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b2">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Olive" title="b1">J</font>,<span class="p1">(<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><br/>

<span class="kw">set </span><font color="Maroon" title="c8">FL</font> = <font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">FLV</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c6">V1</font> as   <a href="matrixj2.html#V2" title="MATRIXJ2:attr.2">nilpotent</a>  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c6">V1</font>,<font color="Maroon" title="c6">V1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="matrixj2.html#T14" target="_self" title="MATRIXJ2:th.14">Th14</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E39">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">FLV</font> implies <font color="Maroon" title="c9">FLV</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:52_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">FLV</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">FLV</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">v1</font> = <font color="Maroon" title="c10">x</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c6">V1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">v</font> = <font color="Maroon" title="c11">v1</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c4">V</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T10" title="VECTSP_4:th.10">VECTSP_4:10</a></span>;<br/><a NAME="E4:52_1"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a></span>;<br/><a NAME="E5:52_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A4</font></span>: 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T18" title="FUNCT_1:th.18">FUNCT_1:18</a>, <a class="ref" href="vectsp_4.html#T14" title="VECTSP_4:th.14">VECTSP_4:14</a></span>;<br/><a NAME="E6:52_1"/><span class="lab"><font color="Green" title="E41">A5</font></span>: 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c9">FLV</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D3" title="MATRLIN:def.3">MATRLIN:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c4">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D4" title="MATRLIN:def.4">MATRLIN:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font></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"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E6:52_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="ref" href="vectsp_4.html#T13" title="VECTSP_4:th.13">VECTSP_4:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font></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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D4" title="MATRLIN:def.4">MATRLIN:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D3" title="MATRLIN:def.3">MATRLIN:def 3</a></span>
; <a class="txt" 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 href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">FLV</font> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">V1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E6:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c9">FLV</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">F1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c11">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c6">V1</font><span class="kw"> such that </span><br/><a NAME="E8:52"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c9">FLV</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c10">J</font>,<span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="matrixj2.html#T29" target="_self" title="MATRIXJ2:th.29">Th29</a></span>;<br/>
<a NAME="E9:52"/>
<font color="Maroon" title="c3">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">JM</font> = <font color="Maroon" title="c10">J</font> <a href="matrixj1.html#K25" title="MATRIXJ1:func.25">(+)</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span> as    <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj2.html#T12" target="_self" title="MATRIXJ2:th.12">Th12</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</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="c12">JM</font> implies  not <font color="Maroon" title="c12">JM</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c13">x</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:52_3"/><span class="lab"><font color="Green" title="E42">A8</font></span>: 
<font color="Maroon" title="c13">x</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="c12">JM</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c12">JM</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c13">x</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">reconsider </span><font color="Maroon" title="c14">i</font> = <font color="Maroon" title="c13">x</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_3"><span class="lab"><font color="Green" title="E42">A8</font></span></a></span>;<br/><a NAME="E3:52_3"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
<font color="Maroon" title="c12">JM</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c14">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c14">i</font></span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p3">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c14">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_3"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="ref" href="matrixj1.html#D10" title="MATRIXJ1:def.10">MATRIXJ1:def 10</a></span>;<br/><a NAME="E4:52_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c12">JM</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">J</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D10" title="MATRIXJ1:def.10">MATRIXJ1:def 10</a></span>;<br/><a NAME="E5:52_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c14">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_3"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="ref" href="funct_1.html#D9" title="FUNCT_1:def.9">FUNCT_1:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E6:52_3"/>
 not <font color="Maroon" title="c12">JM</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c13">x</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_3"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></span>; <a class="txt" 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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">JM</font> = <font color="Maroon" title="c12">JM</font> as   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D9" title="FUNCT_1:def.9">FUNCT_1:def 9</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c13">JM</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c6">V1</font> st  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b1">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c13">JM</font>,<span class="p1">(<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><br/>

<span class="kw">take </span>
<font color="Maroon" title="c11">b1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c13">JM</font>,<span class="p1">(<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><br/>

<span class="kw">set </span><font color="Maroon" title="c14">Aid</font> =  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c15">AF1</font> =  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>);<br/>
<div><span class="lab"><font color="Green" title="E42">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_4"><span class="kw">now </span></a><div class="add"><a NAME="E1:52_4"/><span class="lab"><font color="Green" title="E43">A11</font></span>: 
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</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> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T26" title="MATRIX_1:th.26">MATRIX_1:26</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c16">i</font>, <font color="Maroon" title="c17">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="firebrick">::  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="c16">i</font>,<font color="Maroon" title="c17">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> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>) )</span><br/><span class="kw">assume </span><a NAME="E2:52_4"/><span class="lab"><font color="Green" title="E44">A12</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">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> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span><br/><a NAME="E3:52_4"/>
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></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> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T26" title="MATRIX_1:th.26">MATRIX_1:26</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_4"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</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"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</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="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_4"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</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="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</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="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_4"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="txt" href="#E1:52_4"><span class="lab"><font color="Green" title="E43">A11</font></span></a>, <a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_4"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="txt" href="#E1:52_4"><span class="lab"><font color="Green" title="E43">A11</font></span></a>, <a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D3" title="VECTSP_1:def.3">VECTSP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</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"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T16" title="VECTSP_1:th.16">VECTSP_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T7" title="VECTSP_1:th.7">VECTSP_1:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c16">i</font>,<font color="Maroon" title="c17">j</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
;<br/> <a class="txt" 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="lab"><font color="Green" title="E43">A13</font></span>:  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span> = 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T62" title="MATRIXJ1:th.62">MATRIXJ1:62</a></span>
<br/>.= 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T56" title="MATRIXJ1:th.56">MATRIXJ1:56</a></span>
;<br/>
<a NAME="E15:52"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#D8" title="MATRIXJ1:def.8">MATRIXJ1:def 8</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E44">A14</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>
;<br/>
<span class="lab"><font color="Green" title="E45">A15</font></span>:  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c9">FLV</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="matrixj1.html#D5" title="MATRIXJ1:def.5">MATRIXJ1:def 5</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">b1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D2" title="MATRIX_1:def.2">MATRIX_1:def 2</a></span>
;<br/>
<span class="lab"><font color="Green" title="E46">A16</font></span>:  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p3">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span> = 
 <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p2">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T62" title="MATRIXJ1:th.62">MATRIXJ1:62</a></span>
<br/>.= 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T56" title="MATRIXJ1:th.56">MATRIXJ1:56</a></span>
<br/>.= 
 <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <font color="Maroon" title="c10">J</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T46" title="MATRIXJ1:th.46">MATRIXJ1:46</a></span>
;<br/>
 <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>) = 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T34" title="MATRLIN2:th.34">MATRLIN2:34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T34" title="MATRLIN2:th.34">MATRLIN2:34</a></span>
<br/>.= 
 <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T38" title="MATRLIN2:th.38">MATRLIN2:38</a></span>
;<br/>
<a NAME="E20:52"/><span class="kw">then </span>
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T39" title="MATRLIN2:th.39">MATRLIN2:39</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c9">FLV</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:52"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="matrlin.html#T42" title="MATRLIN:th.42">MATRLIN:42</a></span>
<br/>.= 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:52"><span class="lab"><font color="Green" title="E42">A10</font></span></a>, <a class="ref" href="matrix_1.html#T27" title="MATRIX_1:th.27">MATRIX_1:27</a></span>
;<br/>
<span class="kw">hence </span> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c7">F1</font>,<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c11">b1</font>) = 
<span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c10">J</font>,<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="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p3">(<span class="default"><a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E17:52"><span class="lab"><font color="Green" title="E45">A15</font></span></a>, <a class="ref" href="matrlin2.html#T28" title="MATRLIN2:th.28">MATRLIN2:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c10">J</font>,<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="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<span class="p3">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>,<span class="p3">(<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>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T61" title="MATRIXJ1:th.61">MATRIXJ1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c10">J</font>,<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="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<span class="p2">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p3">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<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>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:52"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="ref" href="matrixj1.html#T65" title="MATRIXJ1:th.65">MATRIXJ1:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c10">J</font>,<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="matrlin2.html#K5" title="MATRLIN2:func.5">+</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<span class="p2">(<span class="default"><a href="matrixj1.html#K24" title="MATRIXJ1:func.24">mlt</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c3">L</font></span>)</span>,<span class="p3">(<span class="default"><a href="matrixj1.html#K23" title="MATRIXJ1:func.23">1.</a> (<font color="Maroon" title="c2">K</font>,<span class="p4">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font></span>)</span>)</span>)</span>)</span>)</span>,<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="vectsp_1.html#T7" title="VECTSP_1:th.7">VECTSP_1:7</a></span>
<br/>.= 
 <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c13">JM</font>,<span class="p1">(<span class="default"><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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="txt" href="#E14:52"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="txt" href="#E18:52"><span class="lab"><font color="Green" title="E46">A16</font></span></a>, <a class="ref" href="matrixj1.html#T72" title="MATRIXJ1:th.72">MATRIXJ1:72</a></span>
<br/>.= 
 <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> (<font color="Maroon" title="c13">JM</font>,<span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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