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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><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">F</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">K</font>  st <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/>( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Olive" title="b2">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Olive" title="b2">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 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="c3">K</font><br/> for <font color="Olive" title="b2">F</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K</font>  st <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/>( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Olive" title="b1">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Olive" title="b1">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">L</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K</font>  st <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> holds <br/>( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">J</font> =  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Ci</font> =  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">N</font> = <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">F</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> implies ( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:10"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) )</span><br/>

<a NAME="E3:10"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">i1</font> = <font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T21" title="NAT_1:th.21">NAT_1:21</a></span>;<br/>
<a NAME="E5:10"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E6:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>;<br/>
<a NAME="E7:10"/><span class="lab"><font color="Green" title="E14">A5</font></span>: 
<font color="Maroon" title="c9">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E8:10"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/>
<a NAME="E9:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A6</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E10:10"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E11:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</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="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">Ci</font> =  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c11">f</font> = <font color="Maroon" title="c8">F</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c7">N</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E13:10"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T144" title="FINSEQ_2:th.144">FINSEQ_2:144</a></span>;<br/>
<a NAME="E14:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c11">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E15:10"/><span class="lab"><font color="Green" title="E20">A11</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T144" title="FINSEQ_2:th.144">FINSEQ_2:144</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E21">A12</font></span>: <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font> = 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E14:10"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="ref" href="fvsum_1.html#T74" title="FVSUM_1:th.74">FVSUM_1:74</a></span>
<br/>.= 
<font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E17:10"/>
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:10_2"/><span class="lab"><font color="Green" title="E22">A13</font></span>: 
( <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c11">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E2:10_2"/><span class="lab"><font color="Green" title="E23">A14</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</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="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:10_2"/><span class="lab"><font color="Green" title="E24">A15</font></span>: 
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> implies <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p3">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10_2_1"/><span class="lab"><font color="Green" title="E25">A16</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">and </span><br/><a NAME="E2:10_2_1"/><span class="lab"><font color="Green" title="E26">A17</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p3">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font></span><br/><a NAME="E3:10_2_1"/><span class="lab"><font color="Green" title="E27">A18</font></span>: 
<font color="Maroon" title="c11">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/><a NAME="E4:10_2_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/><a NAME="E5:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A19</font></span>: 
<font color="Maroon" title="c2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_2"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E6:10_2_1"/><span class="lab"><font color="Green" title="E29">A20</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c2">i</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="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> = 
<span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c2">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_1"><span class="lab"><font color="Green" title="E26">A17</font></span></a>, <a class="txt" href="#E5:10_2_1"><span class="lab"><font color="Green" title="E28">A19</font></span></a>, <a class="txt" href="#E6:10_2_1"><span class="lab"><font color="Green" title="E29">A20</font></span></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a></span>
;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p3">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">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="c3">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E25">A16</font></span></a>, <a class="txt" href="#E3:10_2_1"><span class="lab"><font color="Green" title="E27">A18</font></span></a>, <a class="ref" href="fvsum_1.html#T74" title="FVSUM_1:th.74">FVSUM_1:74</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T36" title="VECTSP_1:th.36">VECTSP_1:36</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> = 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p3">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="ref" href="matrix_3.html#T14" title="MATRIX_3:th.14">MATRIX_3:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="fvsum_1.html#T74" title="FVSUM_1:th.74">FVSUM_1:74</a></span>
<br/>.= 
<font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2"><span class="lab"><font color="Green" title="E23">A14</font></span></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<a NAME="E18:10"/><span class="lab"><font color="Green" title="E22">A21</font></span>: 
<font color="Maroon" title="c9">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font>
 
;<br/>
<span class="kw">assume </span><a NAME="E19:10"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span></span><br/>

<a NAME="E20:10"/><span class="kw">then </span>
<font color="Maroon" title="c9">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<a NAME="E21:10"/><span class="kw">then </span>
<font color="Maroon" title="c9">i1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/>
<a NAME="E22:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A22</font></span>: 
<font color="Maroon" title="c9">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E15">A6</font></span></a></span>;<br/>
<a NAME="E23:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A23</font></span>: 
( <font color="Maroon" title="c9">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c2">i</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="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E25">A24</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">i1</font> implies <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10_3"/><span class="lab"><font color="Green" title="E26">A25</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">and </span><br/><a NAME="E2:10_3"/><span class="lab"><font color="Green" title="E27">A26</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font>
 <span class="kw">and </span><br/><a NAME="E3:10_3"/><span class="lab"><font color="Green" title="E28">A27</font></span>: 
<font color="Maroon" title="c12">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font></span><br/><a NAME="E4:10_3"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c2">i</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="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E1:10_3"><span class="lab"><font color="Green" title="E26">A25</font></span></a>, <a class="txt" href="#E3:10_3"><span class="lab"><font color="Green" title="E28">A27</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A28</font></span>:  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font> = 
<span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c2">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_3"><span class="lab"><font color="Green" title="E27">A26</font></span></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a></span>
<br/>.= 
<font color="Maroon" title="c10">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E1:10_3"><span class="lab"><font color="Green" title="E26">A25</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
;<br/><a NAME="E6:10_3"/>
<font color="Maroon" title="c11">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:10_3"><span class="lab"><font color="Green" title="E26">A25</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">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="c3">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_3"><span class="lab"><font color="Green" title="E26">A25</font></span></a>, <a class="txt" href="#E5:10_3"><span class="lab"><font color="Green" title="E29">A28</font></span></a>, <a class="ref" href="fvsum_1.html#T74" title="FVSUM_1:th.74">FVSUM_1:74</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T36" title="VECTSP_1:th.36">VECTSP_1:36</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E25:10"/><span class="lab"><font color="Green" title="E26">A29</font></span>: 
<font color="Maroon" title="c11">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E22:10"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E26:10"/><span class="lab"><font color="Green" title="E27">A30</font></span>: 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c2">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E22:10"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>;<br/>
<span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">i1</font> = 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K12" title="FVSUM_1:func.12">mlt</a> <font color="Maroon" title="c10">Ci</font>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">i1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E22:10"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c9">i1</font>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">i1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:10"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="txt" href="#E26:10"><span class="lab"><font color="Green" title="E27">A30</font></span></a>, <a class="txt" href="#E25:10"><span class="lab"><font color="Green" title="E26">A29</font></span></a>, <a class="ref" href="fvsum_1.html#T74" title="FVSUM_1:th.74">FVSUM_1:74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">i1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:10"><span class="lab"><font color="Green" title="E24">A23</font></span></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a></span>
<br/>.= 
<font color="Maroon" title="c11">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">i1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E28:10"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Maroon" title="c4">L</font>,<font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E22:10"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="txt" href="#E18:10"><span class="lab"><font color="Green" title="E22">A21</font></span></a>, <a class="txt" href="#E16:10"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E25">A24</font></span></a>, <a class="ref" href="matrix15.html#T7" title="MATRIX15:th.7">MATRIX15:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
