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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V2" title="MATRLIN:attr.2">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b3">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b4">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V2" title="MATRLIN:attr.2">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b2">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b3">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V2" title="MATRLIN:attr.2">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b2">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#V2" title="MATRLIN:attr.2">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Olive" title="b1">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V1</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><font color="Maroon" title="c6">V1</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">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:()"><i><font color="Red">::  thesis: </font></i></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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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/>













<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green" title="E37">A1</font></i>: 
<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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>set </b><font color="Maroon" title="c8">FL</font> = <font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">FLV</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c4">V</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K12" title="MATRLIN2:func.12">|</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> <b>by </b><i><a class="txt" href="#E1:52"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="matrixj2.html#T14" target="_self" title="MATRIXJ2:th.14">Th14</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:52"/><i><font color="Green" title="E39">A3</font></i>: 
 <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>
 <b>by </b><i><a class="ref" href="matrixj2.html#T29" target="_self" title="MATRIXJ2:th.29">Th29</a></i>;<br/>
<a NAME="E6:52"/>
<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>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">JM</font> = <font color="Maroon" title="c10">J</font> <a href="matrixj1.html#K27" title="MATRIXJ1:func.27">(+)</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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> <b>by </b><i><a class="ref" href="matrixj2.html#T12" target="_self" title="MATRIXJ2:th.12">Th12</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E1:52_1"/><i><font color="Green" title="E40">A4</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/><b>reconsider </b><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> <b>by </b><i><a class="txt" href="#E1:52_1"><i><font color="Green" title="E40">A4</font></i></a></i>;<br/><a NAME="E3:52_1"/>
 <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>
 <b>by </b><i><a class="ref" href="matrixj1.html#D10" title="MATRIXJ1:def.10">MATRIXJ1:def 10</a></i>;<br/><a NAME="E4:52_1"/><b>then </b>
( <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>  &amp; <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#K6" title="MATRLIN2:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj1.html#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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> )
 <b>by </b><i><a class="txt" href="#E1:52_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a>, <a class="ref" href="matrixj1.html#D10" title="MATRIXJ1:def.10">MATRIXJ1:def 10</a></i>;<br/><b>hence </b><a NAME="E5:52_1"/>
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>
 <b>by </b><i><a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>then reconsider </b><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> <b>by </b><i><a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c13">JM</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>take </b>
<font color="Maroon" title="c11">b1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<i><font color="Green" title="E40">A5</font></i>:  <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>
<b>by </b><i><a class="txt" href="#E5:52"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="matrixj1.html#D5" title="MATRIXJ1:def.5">MATRIXJ1:def 5</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">b1</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>
;<br/>
<i><font color="Green" title="E41">A6</font></i>:  <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>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">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="c14">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c14">x</font> )</span><br/><b>assume </b><a NAME="E1:52_4"/><i><font color="Green" title="E42">A7</font></i>: 
<font color="Maroon" title="c14">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:()"><i><font color="Red">::  thesis: </font></i></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="c14">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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c14">x</font></span><br/><b>reconsider </b><font color="Maroon" title="c15">v1</font> = <font color="Maroon" title="c14">x</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c6">V1</font> <b>by </b><i><a class="txt" href="#E1:52_4"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">v</font> = <font color="Maroon" title="c15">v1</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c4">V</font> <b>by </b><i><a class="ref" href="vectsp_4.html#T18" title="VECTSP_4:th.18">VECTSP_4:18</a></i>;<br/><a NAME="E4:52_4"/>
( <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c16">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">v</font> &amp; <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c15">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">v1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><a NAME="E5:52_4"/><b>then </b><i><font color="Green" title="E43">A8</font></i>: 
( <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="matrlin2.html#K7" title="MATRLIN2:func.7">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="c16">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="matrlin2.html#K7" title="MATRLIN2:func.7">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="c15">v1</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">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="c15">v1</font> )
 <b>by </b><i><a class="txt" href="#E2:52"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a>, <a class="ref" href="vectsp_4.html#T22" title="VECTSP_4:th.22">VECTSP_4:22</a></i>;<br/><b>thus </b><font color="Maroon" title="c9">FLV</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c16">v</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<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="c16">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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c16">v</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D5" title="MATRLIN:def.5">MATRLIN:def 5</a></i>
<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="c16">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="matrlin2.html#K7" title="MATRLIN2:func.7">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="c16">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D6" title="MATRLIN:def.6">MATRLIN:def 6</a></i>
<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="c15">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="matrlin2.html#K7" title="MATRLIN2:func.7">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="c15">v1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E5:52_4"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="vectsp_4.html#T21" title="VECTSP_4:th.21">VECTSP_4:21</a></i>
<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="c15">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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c15">v1</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D6" title="MATRLIN:def.6">MATRLIN:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">F1</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="c14">x</font>
<b>by </b><i><a class="ref" href="matrlin.html#D5" title="MATRLIN:def.5">MATRLIN:def 5</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E13:52"/><b>then </b><i><font color="Green" title="E42">A9</font></i>: 
<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="matrlin2.html#K8" title="MATRLIN2:func.8">+</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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c6">V1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E11:52"><i><font color="Green" title="E41">A6</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>
<b>set </b><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="matrlin2.html#K7" title="MATRLIN2:func.7">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/>
<b>set </b><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><i><font color="Green" title="E43">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_5"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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/><b>assume </b><a NAME="E1:52_5"/><i><font color="Green" title="E44">A11</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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="E2:52_5"/><i><font color="Green" title="E45">A12</font></i>: 
(  <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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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> &amp;  <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="matrlin2.html#K7" title="MATRLIN2:func.7">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> )
 <b>by </b><i><a class="ref" href="matrix_1.html#T27" title="MATRIX_1:th.27">MATRIX_1:27</a></i>;<br/><b>thus </b><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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="txt" href="#E1:52_5"><i><font color="Green" title="E44">A11</font></i></a>, <a class="txt" href="#E2:52_5"><i><font color="Green" title="E45">A12</font></i></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="txt" href="#E1:52_5"><i><font color="Green" title="E44">A11</font></i></a>, <a class="ref" href="matrix_3.html#D3" title="MATRIX_3:def.3">MATRIX_3:def 3</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="txt" href="#E1:52_5"><i><font color="Green" title="E44">A11</font></i></a>, <a class="txt" href="#E2:52_5"><i><font color="Green" title="E45">A12</font></i></a>, <a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="txt" href="#E1:52_5"><i><font color="Green" title="E44">A11</font></i></a>, <a class="txt" href="#E2:52_5"><i><font color="Green" title="E45">A12</font></i></a>, <a class="ref" href="matrix_3.html#D5" title="MATRIX_3:def.5">MATRIX_3:def 5</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="ref" href="vectsp_1.html#D12" title="VECTSP_1:def.12">VECTSP_1:def 12</a></i>
<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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="ref" href="vectsp_1.html#T63" title="VECTSP_1:th.63">VECTSP_1:63</a></i>
<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>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<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>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<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>
 
<b>by </b><i><a class="ref" href="matrixj1.html#D8" title="MATRIXJ1:def.8">MATRIXJ1:def 8</a></i>;<br/>
<b>then </b><i><font color="Green" title="E44">A13</font></i>:  <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>
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">J</font>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
;<br/>
<i><font color="Green" title="E45">A14</font></i>:  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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>
<b>by </b><i><a class="ref" href="matrixj1.html#T62" title="MATRIXJ1:th.62">MATRIXJ1:62</a></i>
<br/>.= 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T56" title="MATRIXJ1:th.56">MATRIXJ1:56</a></i>
;<br/>
<i><font color="Green" title="E46">A15</font></i>:  <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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>
<b>by </b><i><a class="ref" href="matrixj1.html#T62" title="MATRIXJ1:th.62">MATRIXJ1:62</a></i>
<br/>.= 
 <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c10">J</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T56" title="MATRIXJ1:th.56">MATRIXJ1:56</a></i>
<br/>.= 
 <a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <font color="Maroon" title="c10">J</font>
<b>by </b><i><a class="ref" href="matrixj1.html#T46" title="MATRIXJ1:th.46">MATRIXJ1:46</a></i>
;<br/>
 <a href="matrlin2.html#K5" title="MATRLIN2:func.5">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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c6">V1</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin2.html#T34" title="MATRLIN2:th.34">MATRLIN2:34</a></i>
<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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="ref" href="matrlin2.html#T34" title="MATRLIN2:th.34">MATRLIN2:34</a></i>
<br/>.= 
 <a href="matrlin2.html#K5" title="MATRLIN2:func.5">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="ref" href="matrlin2.html#T38" title="MATRLIN2:th.38">MATRLIN2:38</a></i>
;<br/>
<a NAME="E20:52"/><b>then </b>
 <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="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
 
<b>by </b><i><a class="ref" href="matrlin2.html#T39" title="MATRLIN2:th.39">MATRLIN2:39</a></i>;<br/>
<b>then </b><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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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#K6" title="MATRLIN2:func.6">+</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="matrlin2.html#K7" title="MATRLIN2:func.7">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>
<b>by </b><i><a class="txt" href="#E13:52"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="matrlin.html#T47" title="MATRLIN:th.47">MATRLIN:47</a></i>
<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>
<b>by </b><i><a class="txt" href="#E14:52"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="matrix_1.html#T28" title="MATRIX_1:th.28">MATRIX_1:28</a></i>
;<br/>
<b>hence </b> <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#K6" title="MATRLIN2:func.6">+</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>
<b>by </b><i><a class="txt" href="#E5:52"><i><font color="Green" title="E39">A3</font></i></a>, <a class="txt" href="#E10:52"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="matrlin2.html#T28" title="MATRLIN2:th.28">MATRLIN2:28</a></i>
<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#K6" title="MATRLIN2:func.6">+</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>
<b>by </b><i><a class="ref" href="matrixj1.html#T61" title="MATRIXJ1:th.61">MATRIXJ1:61</a></i>
<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#K6" title="MATRLIN2:func.6">+</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#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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>
<b>by </b><i><a class="txt" href="#E16:52"><i><font color="Green" title="E44">A13</font></i></a>, <a class="ref" href="matrixj1.html#T65" title="MATRIXJ1:th.65">MATRIXJ1:65</a></i>
<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#K6" title="MATRLIN2:func.6">+</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#K25" title="MATRIXJ1:func.25">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="finseqop.html#K4" title="FINSEQOP:func.4">|-&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>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<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>
<b>by </b><i><a class="txt" href="#E17:52"><i><font color="Green" title="E45">A14</font></i></a>, <a class="txt" href="#E18:52"><i><font color="Green" title="E46">A15</font></i></a>, <a class="ref" href="matrixj1.html#T72" title="MATRIXJ1:th.72">MATRIXJ1:72</a></i>
<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>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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