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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">d1</font>, <font color="Olive" title="b2">d2</font>, <font color="Olive" title="b3">d3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> holds  <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Olive" title="b3">d3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of 3,1,<font color="Maroon" title="c1">D</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">d1</font>, <font color="Maroon" title="c3">d2</font>, <font color="Maroon" title="c4">d3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c2">d1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c3">d2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c4">d3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of 3,1,<font color="Maroon" title="c1">D</font></span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">p</font> = <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c2">d1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>, <font color="Maroon" title="c6">q</font> = <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c3">d2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>, <font color="Maroon" title="c7">r</font> = <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c4">d3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> ;<br/>
<a NAME="E2:36"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">p</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> <font color="Maroon" title="c6">q</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> <font color="Maroon" title="c7">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T40" onmouseover="rs('finseq_1/T40')" onmouseout="rh()">FINSEQ_1:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:36"/>
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c2">d1</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c3">d2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>,<span class="p2"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c4">d3</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> is   <a href="matrix_0.html#NM2" title="MATRIX_0:NM.2">Matrix</a> of 3,1,<font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixr2.html#T34" onmouseover="rs('matrixr2/T34')" onmouseout="rh()">MATRIXR2:34</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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