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<b>reconsider </b><font color="Maroon" title="c3">JJ</font> = <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><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="c2">L</font>,1</span>)</span></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> as    <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> <b>by </b><i><a class="ref" href="matrixj2.html#T11" target="_self" title="MATRIXJ2:th.11">Th11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">JJ</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">JJ</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">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="c4">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="c3">JJ</font> implies  not <font color="Maroon" title="c3">JJ</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c4">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/><b>assume </b><a NAME="E1:21_1_1_1"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c4">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="c3">JJ</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="c3">JJ</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c4">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/><a NAME="E2:21_1_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">JJ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default">1</span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E3:21_1_1_1"/><b>then </b>
( <font color="Maroon" title="c3">JJ</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> 1 <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>,1 &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <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="c2">L</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="txt" href="#E1:21_1_1_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="matrixj2.html#D1" target="_self" title="MATRIXJ2:def.1">Def1</a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:21_1_1_1"/>
not <font color="Maroon" title="c3">JJ</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Maroon" title="c4">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <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>hence </b><a NAME="E3:21_1_1"/>
<font color="Maroon" title="c3">JJ</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D15" title="FUNCT_1:def.15">FUNCT_1:def 15</a></i>; <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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