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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">m</font>, <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> &amp; <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/><span class="p1"><a href="matrix14.html#NK3" title="MATRIX14:NK.3">|(</a><span class="default"><span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">i</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">i</font>)</span>)</span></span><a href="matrix14.html#NK3" title="MATRIX14:NK.3">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">K</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font> implies <span class="p1"><a href="matrix14.html#NK3" title="MATRIX14:NK.3">|(</a><span class="default"><span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span></span><a href="matrix14.html#NK3" title="MATRIX14:NK.3">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">K</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</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="matrix14.html#NK3" title="MATRIX14:NK.3">|(</a><span class="default"><span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span></span><a href="matrix14.html#NK3" title="MATRIX14:NK.3">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">K</font></span><br/>

<a NAME="E2:41"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix14.html#T23" target="_self" onmouseover="rs('matrix14/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">hence </span><span class="p1"><a href="matrix14.html#NK3" title="MATRIX14:NK.3">|(</a><span class="default"><span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span></span><a href="matrix14.html#NK3" title="MATRIX14:NK.3">)|</a></span> = 
<span class="p1">(<span class="default"><a href="matrix14.html#K3" title="MATRIX14:func.3">Base_FinSeq</a> (<font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="matrix14.html#T35" target="_self" onmouseover="rs('matrix14/T35')" onmouseout="rh()">Th35</a></span>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">K</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="matrix14.html#T24" target="_self" onmouseover="rs('matrix14/T24')" onmouseout="rh()">Th24</a></span>
;<br/> <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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