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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_2_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> implies  ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> (<font color="Maroon" title="c2">L</font>,<font color="Olive" title="b1">k</font>) )</span><br/><span class="kw">assume </span><a NAME="E1:27_2_1_1"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> (<font color="Maroon" title="c2">L</font>,<font color="Olive" title="b1">k</font>)</span><br/><a NAME="E2:27_2_1_1"/>
<font color="Maroon" title="c5">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">J</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_2_1_1"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="finseq_5.html#T26" title="FINSEQ_5:th.26">FINSEQ_5:26</a></span>;<br/><a NAME="E3:27_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A2</font></span>: 
( <font color="Maroon" title="c3">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">i</font></span>)</span> &amp;  ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c3">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> (<font color="Maroon" title="c2">L</font>,<font color="Olive" title="b1">k</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj2.html#D3" target="_self" title="MATRIXJ2:def.3">Def3</a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><a NAME="E4:27_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_2_1_1"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">hence </span><a NAME="E5:27_2_1_1"/>
 ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="matrixj2.html#K5" title="MATRIXJ2:func.5">/^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> (<font color="Maroon" title="c2">L</font>,<font color="Olive" title="b1">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_2_1_1"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:27_2_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="finseq_5.html#T27" title="FINSEQ_5:th.27">FINSEQ_5:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:27_2_1"/>
<font color="Maroon" title="c3">J</font> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> <font color="Maroon" title="c4">n</font> is    <a href="matrixj2.html#M1" title="MATRIXJ2:mode.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">L</font>,<font color="Maroon" title="c1">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj2.html#D3" target="_self" title="MATRIXJ2:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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